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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