Question

what is the size of the population at t=1000days when the population size at t days is given by the function s(t)=Ae^(kt)
s(0)=1000
s(500)=7000

Answer 1

The s(0) tells you the initial population, which is A.\[s(t)=1000e^{kt}\]Plug in t = 500 and s(500) = 7000 and solve for k.\[7000 = 1000e^{500k}\]\[k = \frac {1}{500} \ln 7 \approx 0.0038918203\]So your function is \[s(t) = 1000e^{0.0038918203t}\]You want to find the population when t = 1000 days, so plug that into your function.\[s(1000) = 1000e^{0.0038918203\times 1000} = 49000\]

Answer 2

Thank u!

Answer 3

should it not be ln 7000

Answer 4

ok i got it! never mind

Answer 5

Your welcome :) There is an easier way to do this though :P from t = 0 to t = 500, the population grew 7 times. So the population grows 7 times every 500 days. From t= 500 to t = 1000, is another 500 days, so its going to be 7 times the population at t = 500, which would be 7000 x 7 = 49000. Much easier than doing all that exponential function stuff.

Answer 6

i never looked at it that way! thank you!