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Math: Calculus

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Assume that a population size at time t is N(t) and that N(t)=40 x 2^t , t>0.

Show that N(t)=40e^t ln2

Can someone please guide me step by step on this question? Im really confused. thanks.

I tried to work it out, and this is what I got.

N(t)= 40 x 2^t
= 40 x ln 2^t
= 40 x t ln 2

  • Math: Calculus -

    changing the base of a log: Alg II

  • Math: Calculus -

    I'm sorry, I still don't understand

  • Math: Calculus -

    by definition, 2 = e^(ln 2)

    Therefore, 2^t = e^(ln 2)^t = e^(t ln 2)

    Make sense yet?

    Now, ln (2^t) = t * ln 2

    So, ln N = ln 40 + t ln 2

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