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Math Help - Exponential Growth and Decay (word problems).

  1. #1
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    Exclamation Exponential Growth and Decay (word problems).

    1) "Solve the equation: The price of a new car is $28,000 and it depreciates 9% each year. How much is the car worth in 6 years?"

    I THINK #1 is as follows...

    y = 28,000(1+/-0.09)^6
    y = 28,000(+/-1.09)^6
    y = 28,000(1.678)
    y = 46,984
    And this looks completely wrong to me.


    2) "Solve the equation: A population of 175 snails is increasing at an annual rate of 12%. At this rate, how long will it take for the population of snails to reach 315?"

    I have absolutely no idea.



    I know that I should apply the formulas y = ae^+/-kt and y = a(1+/-r)^t, but I'm not quite sure for which type of problem uses which formula. I do believe that y = a(1+/-r)^t is used for money, but again, I'm just stuck on how to do these. Thanks in advance to anyone who'll tackle these.
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  2. #2
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    Quote Originally Posted by Mulya66 View Post
    1) "Solve the equation: The price of a new car is $28,000 and it depreciates 9% each year. How much is the car worth in 6 years?"

    I THINK #1 is as follows...

    y = 28,000(1+/-0.09)^6
    The car depreciates at 9%, so the rate of growth of value is -0.09 so in six years the car is worth:

    y = 28000(1 - 0.09)^6 = 28000 0.91^6 ~= 15900.34

    y = 28,000(+/-1.09)^6
    y = 28,000(1.678)
    y = 46,984
    1+/-0.09 is 0.91 or 1.09, not +/-1.09


    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Mulya66 View Post
    1) 2) "Solve the equation: A population of 175 snails is increasing at an annual rate of 12%. At this rate, how long will it take for the population of snails to reach 315?"
    After N years the population is:

    P(N) = 175 (1+0.12)^N.

    If the population after N years is 315 then we hav:

    315 = 175 (1.12)^N

    which we have to solve.

    rearranging this gives:

    (1.12)^N = 315/175 = 1.8

    Now take logs:

    N log(1.12) = log(1.8),

    so:

    N = log(1.8)/log(1.12) ~= 5.19 years.

    RonL
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  4. #4
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    Oh okay, now I understand my error in #1.

    Thank you!
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