In calendar year 2004, Division A of MegaStore increased its sales from $1.5 billion to $1.8 billion, and Division B increased i

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4 years ago

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In calendar year 2004, Division A of MegaStore increased its sales from $1.5 billion to $1.8 billion, and Division B increased i

ts sales from $600 million to $1.0 billion. If each division continues to increase sales by these amounts, when will the two divisions have equal sales? What will be the common value of the sales?finite math

Mathematics

1 answer:

german · Answer 1 · 2021-12-16T05:55:15+03:00

A’s increase is 1.8/1.5=6/5; B’s increase is 1/0.6=5/3.
A formula for A is A(t)=1.5(6/5)^t and for B, B(t)=0.6(5/3)^t where t is years since 2004.
When A=B, 1.5(6/5)^t=0.6(5/3)^t.
Taking logs: log1.5+tlog(6/5)=log0.6+tlog(5/3), t(log(5/3)-log(6/5))=log1.5-log0.6.
tlog(25/18)=log2.5, t=log2.5/log(25/18)=2.7893 approx.
This occurs during 2006 around mid-October.
Common sales=1.5(6/5)^2.7893=0.6(5/3)^2.7893=$2.4943 billion.