Question

After a devastating winter, when thousands of fish died, an environmental scientist has replenished the trout stock in a fishing pond. He started with 8,000 baby trout and has finished a count to find that, in 5 years, the population is estimated to be 24,000. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new trout population?

Hint: A(t) = A0(1+r)^t, where A(t) is the final amount, A0 is the initial amount, r is the growth rate expressed as a decimal, and t is time.

A. 33.3%
B. 2.5%
C. 60.0%
D. 24.6%

Answer 1

you just need to solve for r in that equation
\[A(t)=A_0 (1+r)^t\]
in five years we have \[A(5)=8000(1+r)^5\]
\[24000=8000(1+r)^5 \]

Answer 2

can you solve for r?

Answer 3

I think so

Answer 4

\[r = -1 + \sqrt[5]{3}\]

Answer 5

@xapproachesinfinity Is that right?

Answer 6

so what is the value?

Answer 7

I'm not 100% sure. Could you maybe walk me through this? I don't really understand. If you have time at least

Answer 8

you already did half the work just use calculator

Answer 9

Ok one sec

Answer 10

I got 0.2457

Answer 11

you need to multiply by 100

Answer 12

So 24.57

Answer 13

so?

Answer 14

So the last choice?

Answer 15

yes

Answer 16

Thank you for your help