Answer
$\approx 7347$
$1.08^{n}(5000)$
Work Step by Step
"x increases by $ 8\%$" = " the new value is $ 108\%$ of x"
(=1.08x)
Initially, (after 0 hours), $a_{1}=a=5000$
after 1 hours: $a_{2}=1.08a=1.08(5000)$
after 2 hours: $a_{3}=1.08a_{2}=1.08^{2}a=1.08^{2}(5000)$
after 3 hours: $a_{4}=1.08a_{3}=1.08^{3}a=1.08^{3}(5000)$
...
This pattern defines
$a_{n}$ = number of bacteria after $\mathrm{n}-1$ hours
After 5 hours,
$a_{6}= 1.08^{5}(5000)\approx$7346.640384s$\approx 7347$
After n hours:
$ a_{n+1}=1.08^{n}(5000)$
