Question

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 3% per hour. Suppose that a sample culture has an initial population of 428 bacteria. Find the predicted population after six hours. Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

The predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

A continuous exponential growth model is used to determine the final value of a quantity (V), from an initial value of the quantity (V₀), at a rate of continuous growth per unit time (r), after the time (t), as:

$V = V_0e^{rt}$.

In the question, we are given that the number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 3% per hour.

We are asked, to find the predicted population after six hours when the initial population was 428 bacteria.

Thus, we take V₀ = 428, r = 3% = 0.03, and t = 6, in the equation:

$V = V_0e^{rt}$ ,

to find the predicted population (V) of bacteria after 6 hours.

Thus,

$V = 428e^{0.03*6}\\\Rightarrow V = 428e^{0.18}\\\Rightarrow V = 428*1.1972173631218\\\Rightarrow V = 512.40903141613\\\Rightarrow V = 512.4$

Rounding to the nearest tenth.

Thus, the predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

Learn more about the continuous exponential growth model at

brainly.com/question/9235073

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