Section 2.1: Linear Models

Question

Question 5:

A population of beetles is growing according to a linear growth model. Initially, there were 32 beetles, and 10 weeks later, there were 38 beetles.

(a) Write a linear model to describe the number of beetles over time, using weeks as the unit of time.

 =   

(b) How many beetles are there expected to be 13 weeks after the initial point? 

beetles

(c) When do you expect the number of beetles to reach 85? Round your answer to the nearest week.

After  weeks

Answer 1

P(t) = 32 + 3t/5

where t= number of weeks and P = number of beetles

P(13) = 32 + 3(13)/5 = 32+39/5 = 32 +7.8 = 39.8

= 40, rounded off, about 40 beetles in 13 weeks

85 = 32 + 3t/5

425 = 160 + 3t

3t = 425-160= 265

t = 265/3 = about 88 weeks