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    Applications of Functions Word Problems

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    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.

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    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) = ...

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