
Arturo O. answered 10/04/17
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If it decreases by 1/4, that means you have 3/4 as much left as when the month began. The correct equation is
A(t) = 80,000 (3/4)t = 80,000 (0.75)t
Set A(t) = 33,750 and solve for t using logarithms.
33,750 = 80,000 (0.75)t
0.4219 ≅ 0.75t
log(0.4219) = t log(0.75)
t = log(0.4219) / log(0.75) ≅ 3.00 months