Question

A culture started with 1,500 bacteria. After 5 hours it grew to 2,300 bacteria. How many bacteria with be present after 12 hours? PLSSS

Answer 1

4185

Explanation:

A culture of bacteria grows exponentially according to the following general exponential growth function;

`P_(t)=P_(0)e^(kt)`

where;

p(t) is the population at any given time t.

p(0) is the initial population

k is the growth constant

From the information given we have;

p(0) = 1500

at t = 5, p(t) = 2300; p(5) = 2300

We shall use this information to determine the value of k;

`2300=1500e^(5k)`

Divide both sides by 1500;

`(23)/(15)=e^(5k)\\\\ln((23)/(15))=5k\\\\k=0.08549`

Therefore, the population of the bacteria at any time t is given by;

`P_(t)=1500e^(0.08549t)\\\\P(12)=1500e^(0.08549(12))=4184.3`