Question

An online retail company tracked its monthly purchases, where the number of purchases, p (in thousands), follows a linear model of the form p = S(t) = rt + i, with t representing the months where January 2007 is considered month 0. In March 2007, there were 3,840 purchases (p = 3.84), and in September 2008, there were 4,200 purchases (p = 4.2). What is the rate of change, r, in the linear model for the number of monthly purchases?

A) 0.02
B) 0.03
C) 0.04
D) 0.05

Answer 1

A) 0.02. The rate of change in the linear model for the number of monthly purchases is approximately 0.02.

Step-by-step explanation:

The linear model for the number of monthly purchases is given by p = rt + i, where p is the number of purchases (in thousands), t is the number of months since January 2007, r is the rate of change, and i is the initial number of purchases in January 2007.

To find the rate of change, we can use the given data points. In March 2007 (t = 2), there were 3,840 purchases (p = 3.84), and in September 2008 (t = 20), there were 4,200 purchases (p = 4.2).

Substituting these values into the linear model equation, we get:

3.84 = r*2 + i

4.2 = r*20 + i

Subtracting the first equation from the second equation, we eliminate the initial number of purchases (i):

4.2 - 3.84 = (r*20 + i) - (r*2 + i)

0.36 = 18r

Dividing both sides by 18, we find that r ≈ 0.02

Therefore, the rate of change in the linear model for the number of monthly purchases is approximately 0.02, option A.