Question

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

Answer 1

Answer:

P(n)=5n+9

Step-by-step 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.

$m =\dfrac{44-9}{5-0} =\dfrac{35}{5}\\ Growth per week, m = 5 beetles per week$

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