RaySix

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Exponential Bacteria Growth Model

at November 15th 2023, 8:34:35 pm.

Question: A bacteria culture initially contains 500 bacteria and grows at a rate of 10% per hour. Write the exponential growth model for the number of bacteria, and determine the number of bacteria present after 3 hours.

Answer: The exponential growth model for the number of bacteria can be represented by the equation:

N(t) = N_0 \times e^{kt}

Where:

$N(t)$ = the number of bacteria at time $t$
$N_0$ = the initial number of bacteria (500 in this case)
$k$ = the growth rate (10% or 0.10 in decimal form)
$t$ = time in hours
$e$ = Euler's number, approximately equal to 2.718

Using the given information, the exponential growth model for this bacteria culture is:

N(t) = 500 \times e^{0.10t}

To determine the number of bacteria present after 3 hours, we evaluate the exponential function at $t = 3$ :

N(3) = 500 \times e^{0.10(3)}

N(3) = 500 \times e^{0.30}

N(3) \approx 500 \times 1.3499

N(3) \approx 674.95

Therefore, the number of bacteria present after 3 hours is approximately 674.95.