$[3\mathrm{.}15/4$ Points$]$

SCALC$96\mathrm{.}5\mathrm{.}003.925.$

$($a$)$ Find an expression for the number of bacteria after $t$ hours. $($Round your numeric values to four decimal places.$)$

$P(t)=50e^{(\frac{ln(18\mathrm{.}5)}{1\mathrm{.}5})t}$

$($b$)$ Find the number of bacteria after $4$ hours. $($Round your answer to the nearest whole number.$)$

$P(4)=$

$$ bacteria

$($c$)$ Find the rate of growth $($in bacteria per hour$)$ after $4$ hours. $($Round your answer to the nearest whole number.$)$

$P^{\text{'}}(4)$ bacteria per hour

$($d$)$ After how many hours will the population reach $250,000?($Round your answer to one decimal place.$)$

$t=$

$$ hr

Enhanced Feedback

Please try again. Recall that a bacteria culture with growth rate proportional to the size of the culture has a growth function in the form of $P(t)=P(0)e^{kt},$ where $P(0)$ is the initial value and $k$ is the growth rate.

Find $k$ by replacing other values in the equation with given values from the problem.

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