Question

A population of beetles are growing according to a linear growth model. The initial population (week 0) is Po = 9, and the population after 4 weeks is P4 = 25. Find an explicit formula for the beetle population after n weeks. Pn = After how many weeks will the beetle population reach 113?

Answer 1

Pn = 4n + 9

it will take 26 weeks

Step-by-step explanation:

Po = 9

P4 = 25

the linear model will be in the form of linear equation:

y = mx + c

where c = Po

x = 4

y = P4 = 25

we insert to get the m = slope or rate of change

25 = m(4) + 9

25 = 4m + 9

25 - 9 = 4m

16 = 4m

m = 16/4

m = 4

Inserting the m and c into the equation of line:

y = 4x + 9

We are told represent the number of weeks with n. Hence, we replace our x with n.

Also, y = Pn

Pn = 4n + 9

when Pn = 113, n = ?

Pn = 4n + 9

113 = 4n + 9

113 - 9 = 4n

104 = 4n

104/4 = n

n = 26

Therefore, it will take 26 weeks for the beetle population to reach 113