Answer:
[tex]P= 8n +9[/tex]
Step-by-step explanation:
given that a population of beetles are growing according to a linear growth model.
i.e. P and n are linearly related where P represents the population at time n in weeks.
P(0) = 9 and P(7) = 65
i.e. (0,9) and (7,65) lie on the line of population.
Using two point formula we can find the equation of straight line connecting P and n as
[tex]\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}[/tex]
substitute the given points for (x1,y1) and (x2,y2)
[tex]\frac{P-9}{65-9} =\frac{n-0}{7-0}\\P-9 = \frac{56}{7} (n)\\P= 8n +9[/tex]
Thus
[tex]P= 8n +9[/tex] is the linear equation for the beetle population after n weeks.
