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:
[tex]V = V_0e^{rt}[/tex].
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:
[tex]V = V_0e^{rt}[/tex] ,
to find the predicted population (V) of bacteria after 6 hours.
Thus,
[tex]V = 428e^{0.03*6}\\\Rightarrow V = 428e^{0.18}\\\Rightarrow V = 428*1.1972173631218\\\Rightarrow V = 512.40903141613\\\Rightarrow V = 512.4[/tex]
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
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