Question

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N(t) still alive after t years is given by an exponential function. For Pacific halibut, N(t) = N(0)e-0.2t, where N(0) is the initial size of the cohort. Approximate the percentage of the original number still alive after 13 years. (Give the answer correct to two decimal places.)

Answer 1

So we are given an equation that represents the population of fish left after so many years, so lets plug in t = 13 and see what happens:
\[N(13) = N_{0}e^{-.2(13)}\approx (.074)N_{0}\]
The percentage of the fish still alive is then:
\[\frac{(.074)N_{0}}{N_{0}} (100) = 7.4 \%\]

Answer 2

7.4_% two decimal places.... Thanks so far XD

Answer 3

Nevermind it's 7.43% thanks!