## Calculus: Early Transcendentals 8th Edition

a) $f^{-1}(n)=3\log_2 \frac{n}{100}$, the time elapsed when there are $n$ bacteria. b) The population reaches 50000 after approximately 26 hours 54 mins
a) $n=f(t)=100\cdot 2^\frac{t}{3}$ $2^\frac{t}{3}=\frac{n}{100}$ $\frac{t}{3}=\log_2 \frac{n}{100}$ $f^{-1}(n)=t=3\log_2 \frac{n}{100}$ This expresses the time elapsed when there are $n$ bacteria. b) $n=50000,$ $t=3\log_2 \frac{50000}{100}$ $=3\frac{\ln500}{\ln2}$ $\approx26.897$ hours $\therefore$ the population reaches 50000 after approximately 26 hours 54 mins