The number of bacteria growing in an incubation culture increases with time according to n left parenthesis t right parenthesis equals 2 comma 400 left parenthesis 5 right parenthesis superscript t baseline comma where t is time in days. after how many days will the number of bacteria in the culture be 60 comma 000 ?

For this case we have the following function:

n (t) = 2400 * (5) ^ t

For n (t) = 60000 we have:

60000 = 2400 * (5) ^ t

We clear the value of t.

For this we use the logarithm:

(5) ^ t = 60000/2400

log5 ((5) ^ t) = log5 (60000/2400)

t = log5 (60000/2400)

t = 2 days

Answer:

the number of bacteria in the culture will be 60 comma 000 after:

t = 2 days