Respuesta :
Answer:
4185
Step-by-step explanation:
A culture of bacteria grows exponentially according to the following general exponential growth function;
[tex]P_{t}=P_{0}e^{kt}[/tex]
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;
[tex]2300=1500e^{5k}[/tex]
Divide both sides by 1500;
[tex]\frac{23}{15}=e^{5k}\\\\ln(\frac{23}{15})=5k\\\\k=0.08549[/tex]
Therefore, the population of the bacteria at any time t is given by;
[tex]P_{t}=1500e^{0.08549t}\\\\P(12)=1500e^{0.08549(12)}=4184.3[/tex]
