One model that will work with this problem is f(t) = (0.5)t/h, where t is the length of time decaying, and h is the half-life. In this case, we know f(t) and h, but we do not know t. But we can plug in what we know now and, thanks to logarithms, solve for the missing t.
0.64 = (0.5)t/7.5
To solve for an exponent, we can take a logarithm of both sides and use the logarithm rules to simplify and solve.
ln 0.64 = ln (0.5)t/7.5
ln 0.64 = (t/7.5) ln (0.5)
(ln 0.64) / (ln 0.5) = t/7.5
7.5 (ln 0.64) / (ln 0.5) = t
t ≈ 4.829 minutes
