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

Answer:

4185

Step-by-step 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;

$\frac{23}{15}=e^{5k}\\\\ln(\frac{23}{15})=5k\\\\k=0.08549$

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

$P_{t}=1500e^{0.08549t}\\\\P(12)=1500e^{0.08549(12)}=4184.3$