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abruzzese [7]
3 years ago
12

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
Mathematics
1 answer:
Fynjy0 [20]3 years ago
8 0

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

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a. 4
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</span>
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