Question

A population of beetles are growing according to a linear growth model. The initial population (week 0) is P 0 = 9 P0=9, and the population after 7 weeks is P 7 = 65 P7=65. Find an explicit formula for the beetle population after n n weeks.

Answer 1

Answer:

$P= 8n +9$

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

$\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}$

substitute the given points for (x1,y1) and (x2,y2)

$\frac{P-9}{65-9} =\frac{n-0}{7-0}\\P-9 = \frac{56}{7} (n)\\P= 8n +9$

Thus

$P= 8n +9$ is the linear equation for the beetle population after n weeks.