Question

3000 young trout are introduced into a large fishpond. The number of trout still alive after t years is modeled by the formula N(t) = 3000(.9)^t. What is the rate of population decrease when the number of trout in the pond reaches 2000?

A. Approximately 520 trout per year
B. Approximately 211 trout per year (I think this is the answer)
C. Approximately 2000 trout per year
D. Approximately 494 trout per year
E. None of the above

Please tell what is the correct answer.

Answer 1

3000 young trout are introduced into a large fishpond. The number of trout still alive after t years is modeled by the formula N(t) = 3000(.9)^t. What is the rate of population decrease when the number of trout in the pond reaches 2000?

A. Approximately 520 trout per year
B. Approximately 211 trout per year (I chose this)
C. Approximately 2000 trout per year
D. Approximately 494 trout per year
E. None of the above

Am I right?

Answer 2

First you have to know when there are 2000 left
3000(.9)^t = 2000
.9^t = .6666666...
t = 3.848

N'(t) = 3000(.9)^t (ln.9)
N'(3.848) = 3000(.9)^3.85 (ln.9) = -210.68

you are correct