Question

A population numbers 398 organisms initially and increases by 3.4% each year.Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.P =

Answer 1

Data:

• Initial population (P0) = 398

,

• Increase rate: 3.4%

,

• Exponential model for population:

`P=P0\cdot(1+r)^t`

where P0 represents the initial population, r represents the rate, and t represents the number of years of growth.

Procedure

We are given the value of the initial population (P0) and the rate (r). However, to use them in the formula we cannot do it with the rate in units of percentage, it has to be a number.

In order to do so, we have to divide 3.4% by 100%:

`r=(3.4\%)/(100\%)=0.034`

Now that we have the rate, we can replace it in the formula as the initial population does not need any change:

`P=398\cdot(1+0.034)^t`
`P=398\cdot(1.034)^t`

Answer:

`P=398\cdot(1.034)^t`