An office supply corporation is comparing the sales of two of its regional branc
ID: 2863361 • Letter: A
Question
An office supply corporation is comparing the sales of two of its regional branches. In 2002, branch 23-1 million dollars worth of merchandise. Since 2002, the sales of Branch A has increased by 1.8 million dollars jm-t year. Find a formula for A(t), the sales of Branch A, in millions of dollars, t years after 2002. Since 2002, the sales of Branch B has increased by a rate of 5% per year. Find a formula for B(t), the sales of Branch B, in millions of dollars, t years after 2002. The head corporate office has promised to increase the number of employees working at Branch B if its sales ever surpass those of Branch A. Is there a time after 2002 at which the sales at Branch B will be greater than the sales of Branch A? If so, explain why and find when. If not, explain why not.Explanation / Answer
a)
A(t) = 23.1 + 1.8(t-2002), where t>= 2002
where A(t) is given in billion of dollars
b)
B(t) = 23.1(1.05)^(t-2002), where t>= 2002
where B(t) is given in billion of dollars
c) We need to solve
23.1(1.05)^(t-2002) = 23.1 + 1.8(t-2002)
The value will surpass in 2020, hence the sales of Branch B will be increased from Branch A in 2020