An online retail company tracked total number of purchases monthly. In June 2007 they were 4,500 purchases and in September 2008 there were 5,100. The purchases followed a linear model of the form p = S (t) = r t + i where p purchases is in 1000's and t is months where January 2007=0

Complete Question:

An online retail company tracked total number of purchases monthly. In June 2007 they were 4,500 purchases and in September 2008 there were 5,100. The purchases followed a linear model of the form p = S (t) = r t + i where p purchases is in 1000's and t is months where January 2007=0

a) What is the constant rate of sales

b) Write out the linear model function with the parameter values 'p=S (t)

Answer:

a) Rate of sales, r = 40

b) Linear model function, p = s (t) = 40t + 2100

Step-by-step explanation:

p = S (t) = r t + i ... (1)

Since January 2007 corresponds to t = 0, June 2007 corresponds to t = 6

Purchase, p = S (6) = 4500

Substituting these values into equation (1):

6r + i = 4500 ... (2)

September 2008 corresponds to t = 21

Purchase, p = S (21) = 5100

21r + i = 5100 ... (3)

Subtracting equation (2) from equation (3):

15r = 600

r = 600/15

r = 40

a) Therefore, rate of sale, r = 40

Substituting the value of r into equation (2)

6 (40) + i = 4500

i = 4500 - 2400

i = 2100

b) The linear model function is:

p = s (t) = 40t + 2100