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
