$[4\mathrm{.}2/5$ Points$]$

SCALC$96\mathrm{.}5\mathrm{.}002.$

PRACTICE ANOTH

A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in $1885.$ A cell of this bacterium in a nutrient$-$broth medium divides into two cells every $20$ minutes. The initial population of a culture is $50$ cells.

$($a$)$ Find the relative growth rate.

$k=ln(8),h{r}^{-1}$

$($b$)$ Find an expression for the number of cells after $t$ hours.

$P(t)=50e^{ln(8)t}$

$($c$)$ Find the number of cells after $7$ hours.

$$

$104857600$

cells

$($d$)$ Find the rate of growth after $7$ hours. $($Round your answer to the nearest integer.$)$

$$ cells$/$h

$($e$)$ When will the population reach a million cells? $($Round your answer to two decimal places.$)$

$$ h

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