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

Question

Mathematics

Morgan Briggs

15 February, 13:47

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

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Conor Chambers · Answer 1

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.