Maths

Steve - you answered this question earlier for someone else and gave them the formula for how to answer it. I have the same problem in my homework and have used the formula you gave, but have got an answer that does not appear in the answer options.
I got 12.75
Would you be able to show your workings and help me to get the correct answer please?

the population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?
a. 6 . 6 years
b. 1 years
c. 5 . 3 years
d. 2 . 2 years
e. 12.2 years

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  1. Yeah, I noticed that. I can't figure why the closest answer is so far off. To get 12.2 years, r needs to be 9.58%

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  2. amount = original * (1+r)^t
    3 = (1+r)^t
    ln 3 = t ln (1+r)
    t = ln 3 / ln(1+r)

    r = .09

    t = ln 3 / ln(1.09)

    t = 1.0986 / .086178

    t = 12.74 years
    ======================
    check
    3 = 1 * 1.09^12.74 ??????

    3 = 2.997 yes that will do

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