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
