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# 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

- HyLv 78 years agoFavorite 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.