Answer :
Answer:
P(n)=5n+9
Step-by-step explanation:
The initial population (week 0), [tex]P_0=9[/tex]
Population after 5 weeks, [tex]P_5=44[/tex]
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.
[tex]m =\dfrac{44-9}{5-0} =\dfrac{35}{5}\\$Growth per week, m = 5 beetles per week[/tex]
We then have:
y=5n+b
When Number of weeks, n=0, [tex]P_0[/tex]=y=9
Therefore: 9=5(0)+b
b=9
Therefore, our population after n weeks:
P(n)=5n+9