112. Investigate the behavior of the functions g1(x) ! xe , g2(x) ! x2e x, and g3(x) ! x3e x as x S " and as x S #", and find any horizontal asymptotes. Generalize to functions of the form gn(x) ! x ne x, where n is any positive integer. 113. Explain why the graph of an exponential function cannot be the graph of a polynomial function. 114. Explain why the graph of an exponential function cannot be the graph of a rational function.
APPLICATIONS* ★115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest dollar. ★116.
FINANCE A person wishes to have $15,000 cash for a new
car 5 years from now. How much should be placed in an account now if the account pays 9.75% compounded weekly? Compute the answer to the nearest dollar. 117. MONEY GROWTH If you invest $5,250 in an account paying 11.38% compounded continuously, how much money will be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
113. Explain why the graph of an exponential function cannot be the graph of a polynomial function. 114. Explain why the graph of an exponential function cannot be the graph of a rational function.
APPLICATIONS* ★115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest dollar. ★116.
FINANCE A person wishes to have $15,000 cash for a new
car 5 years from now. How much should be placed in an account now if the account pays 9.75% compounded weekly? Compute the answer to the nearest dollar. 117. MONEY GROWTH If you invest $5,250 in an account paying 11.38% compounded continuously, how much money will be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
ing 8% compounded daily and, at the same time, $5,000 is deposited into an account earning 5% compounded daily, will the first account be worth more than the second? If so, when?
APPLICATIONS* ★115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest dollar. ★116.
FINANCE A person wishes to have $15,000 cash for a new
car 5 years from now. How much should be placed in an account now if the account pays 9.75% compounded weekly? Compute the answer to the nearest dollar. 117. MONEY GROWTH If you invest $5,250 in an account paying 11.38% compounded continuously, how much money will be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
ing 8% compounded daily and, at the same time, $5,000 is deposited into an account earning 5% compounded daily, will the first account be worth more than the second? If so, when? ★120.
FINANCE If $4,000 is deposited into an account earning
9% compounded weekly and, at the same time, $6,000 is deposited into an account earning 7% compounded weekly,
★115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest dollar. ★116.
FINANCE A person wishes to have $15,000 cash for a new
car 5 years from now. How much should be placed in an account now if the account pays 9.75% compounded weekly? Compute the answer to the nearest dollar. 117. MONEY GROWTH If you invest $5,250 in an account paying 11.38% compounded continuously, how much money will be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
ing 8% compounded daily and, at the same time, $5,000 is deposited into an account earning 5% compounded daily, will the first account be worth more than the second? If so, when? ★120.
FINANCE If $4,000 is deposited into an account earning
9% compounded weekly and, at the same time, $6,000 is deposited into an account earning 7% compounded weekly, *Round monetary amounts to the nearest cent unless specified otherwise. In all problems involving interest that is compounded daily, assume a 365-day year.
now if the account pays 9.75% compounded weekly? Compute the answer to the nearest dollar. 117. MONEY GROWTH If you invest $5,250 in an account paying 11.38% compounded continuously, how much money will be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
ing 8% compounded daily and, at the same time, $5,000 is deposited into an account earning 5% compounded daily, will the first account be worth more than the second? If so, when? ★120.
FINANCE If $4,000 is deposited into an account earning
9% compounded weekly and, at the same time, $6,000 is deposited into an account earning 7% compounded weekly, *Round monetary amounts to the nearest cent unless specified otherwise. In all problems involving interest that is compounded daily, assume a 365-day year.
be in the account at the end of (A) 6.25 years? (B) 17 years? 118. MONEY GROWTH If you invest $7,500 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of (A) 5.5 years? (B) 12 years? ★119.
FINANCE If $3,000 is deposited into an account earn-
ing 8% compounded daily and, at the same time, $5,000 is deposited into an account earning 5% compounded daily, will the first account be worth more than the second? If so, when? ★120.
FINANCE If $4,000 is deposited into an account earning 9% compounded and, at the Functions same time, $6,000 S E C T I O Nweekly 5–1 Exponential 469is
deposited into an account earning 7% compounded weekly, will the first account be worth more than the second? If so, when?
*Round monetary amounts to the nearest cent unless specified ★otherwise. 121. FINANCE Will an involving investment of $10,000 at 8.9% comIn all problems interest that is compounded pounded dailya ever be worth daily, assume 365-day year. more at the end of any quarter than
an investment of $10,000 at 9% compounded quarterly? Explain.
★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
S E C T I O N 5–1
Exponential Functions
469
will the first account be worth more than the second? If so, when? ★121.
FINANCE Will an investment of $10,000 at 8.9% com-
pounded daily ever be worth more at the end of any quarter than an investment of $10,000 at 9% compounded quarterly? Explain. ★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 9% compounded continuously? ★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the
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x
, ", cve
ot
ot
ld or to
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S E C T I O N 5–1
Exponential Functions
469
will the first account be worth more than the second? If so, when? ★121.
FINANCE Will an investment of $10,000 at 8.9% com-
pounded daily ever be worth more at the end of any quarter than an investment of $10,000 at 9% compounded quarterly? Explain. ★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 9% compounded continuously? ★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the note now if the note gains value at a rate of 10% compounded continuously?
125. MONEY GROWTH Barron’s, a national business and financial weekly, published the following “Top Savings Deposit Yields” for 212 -year certificate of deposit accounts: Gill Savings Richardson Savings and Loan
8.30% (CC) 8.40% (CQ)
so, when? ★121.
FINANCE Will an investment of $10,000 at 8.9% com-
pounded daily ever be worth more at the end of any quarter than an investment of $10,000 at 9% compounded quarterly? Explain. ★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 9% compounded continuously? ★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the note now if the note gains value at a rate of 10% compounded continuously?
125. MONEY GROWTH Barron’s, a national business and financial weekly, published the following “Top Savings Deposit Yields” for 212 -year certificate of deposit accounts: Gill Savings Richardson Savings and Loan USA Savings
8.30% (CC) 8.40% (CQ) 8.25% (CD)
where CC represents compounded continuously, CQ compounded quarterly, and CD compounded daily. Compute the
an investment of $10,000 at 9% compounded quarterly? Explain. ★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 9% compounded continuously? ★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the note now if the note gains value at a rate of 10% compounded continuously?
125. MONEY GROWTH Barron’s, a national business and financial weekly, published the following “Top Savings Deposit Yields” for 212 -year certificate of deposit accounts: Gill Savings Richardson Savings and Loan USA Savings
8.30% (CC) 8.40% (CQ) 8.25% (CD)
where CC represents compounded continuously, CQ compounded quarterly, and CD compounded daily. Compute the value of $1,000 invested in each account at the end of 212 years. 126. MONEY GROWTH Refer to Problem 125. In another issue of Barron’s, 1-year certificate of deposit accounts included: Alamo Savings
8.25% (CQ)
S #", o funcpositive cannot cannot
should 000 for swer to
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nt payey will
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★122.
FINANCE A sum of $5,000 is invested at 13% com-
pounded semiannually. Suppose that a second investment of $5,000 is made at interest rate r compounded daily. Both investments are held for 1 year. For which values of r, to the nearest tenth of a percent, is the second investment better than the first? Discuss. ★123.
PRESENT VALUE A promissory note will pay $30,000 at
maturity 10 years from now. How much should you pay for the note now if the note gains value at a rate of 9% compounded continuously? ★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the note now if the note gains value at a rate of 10% compounded continuously?
125. MONEY GROWTH Barron’s, a national business and financial weekly, published the following “Top Savings Deposit Yields” for 212 -year certificate of deposit accounts: Gill Savings Richardson Savings and Loan USA Savings
8.30% (CC) 8.40% (CQ) 8.25% (CD)
where CC represents compounded continuously, CQ compounded quarterly, and CD compounded daily. Compute the value of $1,000 invested in each account at the end of 212 years. 126. MONEY GROWTH Refer to Problem 125. In another issue of Barron’s, 1-year certificate of deposit accounts included: Alamo Savings Lamar Savings
8.25% (CQ) 8.05% (CC)
Compute the value of $10,000 invested in each account at the end of 1 year. 127. FINANCE Suppose $4,000 is invested at 11% compounded weekly. How much money will be in the account in (A) 12 year? (B) 10 years? Compute answers to the nearest cent. 128. FINANCE Suppose $2,500 is invested at 7% compounded
ould for er to
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paywill
ount will
arn0 is aily, nd?
ning 0 is kly,
★124.
PRESENT VALUE A promissory note will pay $50,000 at
maturity 512 years from now. How much should you pay for the note now if the note gains value at a rate of 10% compounded continuously?
125. MONEY GROWTH Barron’s, a national business and financial weekly, published the following “Top Savings Deposit Yields” for 212 -year certificate of deposit accounts: Gill Savings Richardson Savings and Loan USA Savings
8.30% (CC) 8.40% (CQ) 8.25% (CD)
where CC represents compounded continuously, CQ compounded quarterly, and CD compounded daily. Compute the value of $1,000 invested in each account at the end of 212 years. 126. MONEY GROWTH Refer to Problem 125. In another issue of Barron’s, 1-year certificate of deposit accounts included: Alamo Savings Lamar Savings
8.25% (CQ) 8.05% (CC)
Compute the value of $10,000 invested in each account at the end of 1 year. 127. FINANCE Suppose $4,000 is invested at 11% compounded weekly. How much money will be in the account in (A) 12 year? (B) 10 years? Compute answers to the nearest cent. 128. FINANCE Suppose $2,500 is invested at 7% compounded quarterly. How much money will be in the account in (A) 34 year? (B) 15 years? Compute answers to the nearest cent.
USA Savings
8.25% (CD)
where CC represents compounded continuously, CQ compounded quarterly, and CD compounded daily. Compute the value of $1,000 invested in each account at the end of 212 years. 126. MONEY GROWTH Refer to Problem 125. In another issue of Barron’s, 1-year certificate of deposit accounts included: Alamo Savings Lamar Savings
8.25% (CQ) 8.05% (CC)
Compute the value of $10,000 invested in each account at the end of 1 year. 127. FINANCE Suppose $4,000 is invested at 11% compounded weekly. How much money will be in the account in (A) 12 year? (B) 10 years? Compute answers to the nearest cent. 128. FINANCE Suppose $2,500 is invested at 7% compounded quarterly. How much money will be in the account in (A) 34 year? (B) 15 years? Compute answers to the nearest cent.
value of $1,000 invested in each account at the end of 22 years. 126. MONEY GROWTH Refer to Problem 125. In another issue of Barron’s, 1-year certificate of deposit accounts included: Alamo Savings Lamar Savings
8.25% (CQ) 8.05% (CC)
Compute the value of $10,000 invested in each account at the end of 1 year. 127. FINANCE Suppose $4,000 is invested at 11% compounded weekly. How much money will be in the account in (A) 12 year? (B) 10 years? Compute answers to the nearest cent. 128. FINANCE Suppose $2,500 is invested at 7% compounded quarterly. How much money will be in the account in (A) 34 year? (B) 15 years? Compute answers to the nearest cent.