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
 
 the number of bacteria in the culture will be 60 comma 000 after:
 t = 2 days