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

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.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

the answer is 18.