Could you please help me with this?

Ae^kt - (A and k are constants, t is time)

when t is 3, the answer is 112486.

when t is 7, the answer is 131593

What is the answer when t is 10?

1 Answer

Relevance
  • Hy
    Lv 7
    8 years ago
    Favorite Answer

    The given data tell us that

    A e^3k = 112486

    A e^7k = 131593

    Dividing the second by the first we get

    e^4k = 131593/112486 = 1.169861 (approx)

    Therefore

    e^k = (131593/112486)^(1/4) = 1.040001 (approx)

    Now some people want to proceed to k = ln(1.040001) = 0.04 (approx), however we don't need it because whenever k appears it's in the form e^k

    Thus A e^(3k) = 112486

    A*(e^k)^3 = 112486

    A*(1.040001)^3 = 112486

    A = 99999.48

    I expect the formula is meant to be

    100000e^(0.04t)

    Hence f(10) = A e^(10k)

    .................. = A*(e^k)^10

    .................. = 100000 e^0.4

    .................. = 149182 approx.

    or, using the unrounded values,

    f(10) = 99999.48*(1.040001^10)

    ....... = 148024 approx.

Still have questions? Get your answers by asking now.