Question

It is projected that t years from now, the population of a certain country will
become P(t)= 50e^0.02t million.
(a) At what rate will the population be changing with respect to time 10 years
from now?
(b) At what percentage rate will the population be changing with respect to time
t years from now? Does this percentage rate depend on t or is it constant?

Answer 1

for part (a) find the derivative and then substitute t = 10 to find the rate of change in the population in millions/year

Answer 2

answer is 1.22 million per year

Answer 3

thats correct

Answer 4

do you how to do b?

Answer 5

well you know the derivative, so put that over the original and multiply by 100

\[\frac{f'(t)}{f(t)} \times 100\]

thats my best guess... and you'll find a few things will cancel...

Answer 6

well i know the answer is 2% per year (textbook answer)

Answer 7

well that makes some sense \[= \frac{1e^{0.02t}}{50e^{0.02t}}\times 100 = \frac{1}{50} \times \frac{e^{0.02t}}{e^{0.02t}} \times 100\]

which seems to give an answer of 2%

Answer 8

thank you some much