A culture started with 5,000 bacteria. After 2 hours, it grew to 6,000 bacteria. Predict how many bacteria will be present after 14 hours. Round your answer to the nearest whole number. P=ae^kt


Answer:

There will be approximately 17915 bacteria after 14 hours.

Step-by-step explanation:

Assuming that the bacteria are growing at a exponential rate expressed by the formula:

P = 5000*e^{k*t}

Where 5000 is the initial number of bacteria and t is the time elapsed in hours, we first need to find the value of k. This is done by applying a known point to the function, which would be 2 hours after the start in this case.

6000 = 5000*e^{k*2}\\e^{2*k} = 1.2\\ln(e^{2*k}) = ln(1.2)\\2*k = ln(1.2)\\k = \frac{ln(1.2)}{2} = 0.09116

We can now predict the number of bacteria after 14 hours as shown below:

P = 5000*e^{(0.09116*14)} = 5000*e^{(1.27624)}\\P = 17915.7

There will be approximately 17915 bacteria after 14 hours.


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