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Applications of Functions Word Problems

1. Solve the equation.
3(6 - 3x) = 1/27

2. Use natural logarithms to evaluate the logarithm to the nearest hundredth.
log√4 ^259.5

3. Solve the problem.
Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $45000
with a raise each March 1 of 3 % Chris starts at $33000 with a raise on March 1 of each year of 8%. In what year will Chris' salary exceed Sonja's?

4. Solve the problem.
The sales of a new model of notebook computer are approximated by : S(x) = 5000-13000e^-x/9, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $2,600,000?

5. Solve the problem.
The number of acres in a landfill decreases according to the function B=6300e^-0.05t , where t is measured in years. How many acres will the landfill have after 10 years?

6. If inflation is 6% a year compounded annually, what will it cost in 18 years to buy a house currently valued at $116,000?

7. A municipal bond with a face value of $10,000 in ten years can be purchased now for $5238. Find the simple interest rate. Round to the nearest tenth of a percent.

8. The State Employees' Credit Union offers a 1-year certificate of deposit with an APR (or effective rate) of 5.5%. If interest is compounded quarterly, find the actual interest rate. Round to the nearest tenth of a percent.

9. Solve the problem. Round to the nearest cent.
If Bob deposits $5,000 at the end of each year for 13 years in an account paying 5% interest compounded annually, find the amount he will have on deposit.

10. Solve the problem. Round to the nearest cent.
Larry wants to start an IRA that will have $950,000 in it when he retires in 19 years. How much should he invest semiannually in his IRA to do this if the interest is 13% compounded semiannually?

11. Solve the problem.
Tasha borrowed $15,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 4 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

12. Find the periodic payment that will render the sum.
S = $590,000, interest is 10% compounded semiannually, payments made at the end of each semiannual period for 8 years.

Solution Preview

Please see the attached file.

1. Solve the equation.
3(6 - 3x) = 1/27
Solution:
Take log on both sides, we get
(6-3x) log 3 = log (1/27)
(6-3x) = log(1/27)/ log 3
(6-3x) = -1.43/0.48
(6-3x) = - 2.98
-3x = -2.98-6
-3x = -8.98
x = 2.99

2. Use natural logarithms to evaluate the logarithm to the nearest hundredth.
log√4 ^259.5
Solution:
259.5 log (2)
259.5 (0.3010)
=> 78.11 (Rounded to the nearest hundredth)
3. Solve the problem.
Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $45000
with a raise each March 1 of 3 % Chris starts at $33000 with a raise on March 1 of each year of 8%. In what year will Chris' salary exceed Sonja's?
Solution:

Sonja Chris
After 5-year= 45000(1+0.03)^5 33000(1+0.08)^5 =>
=>45000(1.03)^5 => 33000(1.08)^5
=> 52167.33 =>48487.83

After 7-years
45000(1.03)^7=> 55344.32 33000(1.08)^7=>56556.20

So, in 7-years, Chris' salary exceed Sonja's
(ie) In 2008 , Chris' salary exceed Sonja's
4. Solve the problem.
The sales of a new model of notebook computer are approximated by : S(x) = 5000-13000e^-x/9, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $2,600,000?
Solution:
Here given : S(x) = ...

Solution Summary

Applications of Functions Word Problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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