Question

A population of beetles are growing according to a linear growth model. The initial population (week 0) is P0=9

and the population after 5 weeks is

P5=44

.


Find an explicit formula for the beetle population after

n weeks.


Pn=


After how many weeks will the beetle population reach 177?

Answer 1

P(n)=5n+9

Explanation:

The initial population (week 0),
`P_0=9`

Population after 5 weeks,
`P_5=44`

Since the population is growing according to a linear growth model.

A linear model is of the form: y=mx+b where m is the slope and b is the y-intercept.

First, we determine the population growth per week which is our slope.

`m =(44-9)/(5-0) =(35)/(5)\\$Growth per week, m = 5 beetles per week`

We then have:

y=5n+b

When Number of weeks, n=0,
`P_0`=y=9

Therefore: 9=5(0)+b

b=9

Therefore, our population after n weeks:

P(n)=5n+9