Question

Suppose P(t)represents the population of a certain mosquito colony, where. t is measured in days. The current population of the colony is known to be 574 mosquitos; that is, P(0)=574. If P'(0)=50 mosquitos per day, estimate the size of the population in 10 days.

Answer 1

Answer:

The estimated size of the population in 10 days is of 1372 mosquitos.

Step-by-step explanation:

Population after t days:

The population after t days is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate, as a decimal.

P(0)=574.

So

$P(t) = 574e^{rt}$

P'(0)=50

$P^{\prime}(t) = 574re^{rt}$

Since P'(0)=50

$574r = 50$

$r = \frac{50}{574}$

$r = 0.0871$

So

$P(t) = 574e^{0.0871t}$

Estimate the size of the population in 10 days

This is P(10).

$P(10) = 574e^{0.0871*10} = 1372$

The estimated size of the population in 10 days is of 1372 mosquitos.