4334.2 Exponential FunctionsSolve each problem. See Examples 7-9.97. Future Value Find the future value and interest earned if $8906.54 is invested for9 yr at 3% compounded(a) semiannually(b) continuously.98. Future Value Find the future value and interest earned if $56,780 is invested at2.8% compounded(a) quarterly for 23 quarters(b) continuously for 15 yr.99. Present Value Find the present value that will grow to $25,000 if interest is 3.2%compounded quarterly for 11 quarters.100. Present Value Find the present value that will grow to $45,000 if interest is 3.6%compounded monthly for 1 yr.101. Present Value Find the present value that will grow to $5000 if interest is 3.5%compounded quarterly for 10 yr.102. Interest Rate Find the required annual interest rate to the nearest tenth of a percentfor $65,000 to grow to $65,783.91 if interest is compounded monthly for 6 months.103. Interest Rate Find the required annual interest rate to the nearest tenth of a percentfor $1200 to grow to $1500 if interest is compounded quarterly for 9 yr.104. Interest Rate Find the required annual interest rate to the nearest tenth of a percentfor $5000 to grow to $6200 if interest is compounded quarterly for 8 yr.Solve each problem. See Example 10.105. Comparing Loans Bank A is lending money at 6.4% interest compounded annu-ally. The rate at Bank B is 6.3% compounded monthly, and the rate at Bank C is6.35% compounded quarterly. At which bank will we pay the least interest?106. Future Value Suppose $10,000 is invested at an annual rate of 2.4% for 10 yr.Find the future value if interest is compounded as follows.(a) annually(b) quarterly(c) monthly(d) daily (365 days)(Modeling) Solve each problem. See Example 11.107. Atmospheric Pressure The atmospheric pressure (in millibars) at a given altitude(in meters) is shown in the table.AMitudePressureAltitudePressure10136000472100089970004112000795800035730007019000308ea400061710,000ut owon sn265LEEVSCASO00541Source: Miller, A. and J. Thompson, Elements ofMeteorology, Fourth Edition, Charles E. MerrillPublishing Company, Columbus, Ohio.(a) Use a graphing calculator to make a scatter diagram of the data for atmosphericpressure P at altitude x.(b) Would a linear or an exponential function fit the data better?(c) The following function approximates the data.P(x) = 1013e-0.0001341xUse a graphing calculator to graph P and the data on the same coordinate axes.(d) Use P to predict the pressures at 1500 m and 11,000 m, and compare them tothe actual values of 846 millibars and 227 millibars, respectively.

Question
Asked Nov 13, 2019
146 views

98.

433
4.2 Exponential Functions
Solve each problem. See Examples 7-9.
97. Future Value Find the future value and interest earned if $8906.54 is invested for
9 yr at 3% compounded
(a) semiannually
(b) continuously.
98. Future Value Find the future value and interest earned if $56,780 is invested at
2.8% compounded
(a) quarterly for 23 quarters
(b) continuously for 15 yr.
99. Present Value Find the present value that will grow to $25,000 if interest is 3.2%
compounded quarterly for 11 quarters.
100. Present Value Find the present value that will grow to $45,000 if interest is 3.6%
compounded monthly for 1 yr.
101. Present Value Find the present value that will grow to $5000 if interest is 3.5%
compounded quarterly for 10 yr.
102. Interest Rate Find the required annual interest rate to the nearest tenth of a percent
for $65,000 to grow to $65,783.91 if interest is compounded monthly for 6 months.
103. Interest Rate Find the required annual interest rate to the nearest tenth of a percent
for $1200 to grow to $1500 if interest is compounded quarterly for 9 yr.
104. Interest Rate Find the required annual interest rate to the nearest tenth of a percent
for $5000 to grow to $6200 if interest is compounded quarterly for 8 yr.
Solve each problem. See Example 10.
105. Comparing Loans Bank A is lending money at 6.4% interest compounded annu-
ally. The rate at Bank B is 6.3% compounded monthly, and the rate at Bank C is
6.35% compounded quarterly. At which bank will we pay the least interest?
106. Future Value Suppose $10,000 is invested at an annual rate of 2.4% for 10 yr.
Find the future value if interest is compounded as follows.
(a) annually
(b) quarterly
(c) monthly
(d) daily (365 days)
(Modeling) Solve each problem. See Example 11.
107. Atmospheric Pressure The atmospheric pressure (in millibars) at a given altitude
(in meters) is shown in the table.
AMitude
Pressure
Altitude
Pressure
1013
6000
472
1000
899
7000
411
2000
795
8000
357
3000
701
9000
308
ea
4000
617
10,000
ut owon sn
265
LEEVSCA
SO00
541
Source: Miller, A. and J. Thompson, Elements of
Meteorology, Fourth Edition, Charles E. Merrill
Publishing Company, Columbus, Ohio.
(a) Use a graphing calculator to make a scatter diagram of the data for atmospheric
pressure P at altitude x.
(b) Would a linear or an exponential function fit the data better?
(c) The following function approximates the data.
P(x) = 1013e-0.0001341x
Use a graphing calculator to graph P and the data on the same coordinate axes.
(d) Use P to predict the pressures at 1500 m and 11,000 m, and compare them to
the actual values of 846 millibars and 227 millibars, respectively.
help_outline

Image Transcriptionclose

433 4.2 Exponential Functions Solve each problem. See Examples 7-9. 97. Future Value Find the future value and interest earned if $8906.54 is invested for 9 yr at 3% compounded (a) semiannually (b) continuously. 98. Future Value Find the future value and interest earned if $56,780 is invested at 2.8% compounded (a) quarterly for 23 quarters (b) continuously for 15 yr. 99. Present Value Find the present value that will grow to $25,000 if interest is 3.2% compounded quarterly for 11 quarters. 100. Present Value Find the present value that will grow to $45,000 if interest is 3.6% compounded monthly for 1 yr. 101. Present Value Find the present value that will grow to $5000 if interest is 3.5% compounded quarterly for 10 yr. 102. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to $65,783.91 if interest is compounded monthly for 6 months. 103. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $1200 to grow to $1500 if interest is compounded quarterly for 9 yr. 104. Interest Rate Find the required annual interest rate to the nearest tenth of a percent for $5000 to grow to $6200 if interest is compounded quarterly for 8 yr. Solve each problem. See Example 10. 105. Comparing Loans Bank A is lending money at 6.4% interest compounded annu- ally. The rate at Bank B is 6.3% compounded monthly, and the rate at Bank C is 6.35% compounded quarterly. At which bank will we pay the least interest? 106. Future Value Suppose $10,000 is invested at an annual rate of 2.4% for 10 yr. Find the future value if interest is compounded as follows. (a) annually (b) quarterly (c) monthly (d) daily (365 days) (Modeling) Solve each problem. See Example 11. 107. Atmospheric Pressure The atmospheric pressure (in millibars) at a given altitude (in meters) is shown in the table. AMitude Pressure Altitude Pressure 1013 6000 472 1000 899 7000 411 2000 795 8000 357 3000 701 9000 308 ea 4000 617 10,000 ut owon sn 265 LEEVSCA SO00 541 Source: Miller, A. and J. Thompson, Elements of Meteorology, Fourth Edition, Charles E. Merrill Publishing Company, Columbus, Ohio. (a) Use a graphing calculator to make a scatter diagram of the data for atmospheric pressure P at altitude x. (b) Would a linear or an exponential function fit the data better? (c) The following function approximates the data. P(x) = 1013e-0.0001341x Use a graphing calculator to graph P and the data on the same coordinate axes. (d) Use P to predict the pressures at 1500 m and 11,000 m, and compare them to the actual values of 846 millibars and 227 millibars, respectively.

fullscreen
check_circle

Expert Answer

Step 1

Given, Present value, interest rate and time in quarterly are

help_outline

Image Transcriptionclose

PV $56780 r 2.8%quarterly = 0.028 t 23quarterly

fullscreen
Step 2

Part (a): The formula for Future value and interest are

help_outline

Image Transcriptionclose

PV (1+r and I = FV - PV FV PV Present value FV Future value 1 Interest r rate quarterly t =time in quarterly

fullscreen
Step 3

The Amount...

help_outline

Image Transcriptionclose

FV $56780(1+0.028) $56780(1.028) $56780(1.88730303) $107161.066 I -S107161.066-$56780 = $50381.066

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Algebra

Exponents