The population of fish in a lake is observed to fluctuate during a six month per

ID: 2859241 • Letter: T

Question

The population of fish in a lake is observed to fluctuate during a six month period according to the formula

P(t) = 80000 + 20000?sin?t

where t is time in months. Answer the questions below.

Note that the units are provided outside the answer boxes. You don't have to include them in your answers.

You may find it useful to graph this function on the domain

0 ? t ? 6

months.

If the population is changing at -11,000 fish/month, how many fish are there?
NOTE: There are two possible correct answers.

Large number

small number

P(t) = 80000 + 20000 sin t

dP/dt = -11000

dP/dt = d/dt ( 80000 + 20000 sin t)

dP/dt = 20000cos(t) = -11000

cos(t) = -11/20

t = 2.15316 or 4.13002

Now, plug these back into the population expression....

P(t) = 80000 + 20000 sin t

At t = 2.15316, P = 80000 + 20000 sin (2.15316) = 96703
At t = 4.13002, P = 80000 + 20000 sin (4.13002) = 63297

Larger number ---> 96703
Smaller number ---> 63297

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.