Question

A species of fish was added to a lake. The population size P (t) of this species can be modeled by the following function, where t is the number of years from the

time the species was added to the lake.
P(t)=-2000/1+6e^-0.42
Find the initial population size of the species and the population size after 7 years.
Round your answers to the nearest whole number as necessary.

Initial population size:

Population size after 7 years:

Answer 1

There seems to be a mistake in the provided function for the population size. The function should include the variable t, which represents the number of years from the time the species was added to the lake. Without the variable t, we cannot determine the initial population size or the population size after 7 years.

Assuming that the correct function for the population size is:

P(t) = -2000/(1 + 6e^(-0.42t))

We can find the initial population size by setting t = 0:

P(0) = -2000/(1 + 6e^0) ≈ -480

Rounding to the nearest whole number, the initial population size is -480.

To find the population size after 7 years, we can substitute t = 7 into the function:

P(7) = -2000/(1 + 6e^(-0.42*7)) ≈ 838

Rounding to the nearest whole number, the population size after 7 years is 838.