Respuesta :
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:
[tex]P = 5000*e^{k*t}[/tex]
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.
[tex]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[/tex]
We can now predict the number of bacteria after 14 hours as shown below:
[tex]P = 5000*e^{(0.09116*14)} = 5000*e^{(1.27624)}\\P = 17915.7[/tex]
There will be approximately 17915 bacteria after 14 hours.
