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Answer :
Answer:
About 6.4 hours.
Step-by-step explanation:
We are given the function:
[tex]\displaystyle B(h) = 1425e^{0.15h}[/tex]
Which measures the population of bacteria B after h hours.
We want to determine the number of hours it will take for the population to reach 3700 bacteria.
Thus, substitute 3700 for B and solve for h:
[tex]\displaystyle \begin{aligned} (3700) & = 1425e^{0.15h} \\ \\ e^{0.15h} & = \frac{3700}{1425} \end{aligned}[/tex]
Take the natural log of both sides. This cancels the e on the left-hand side:
[tex]\displaystyle \begin{aligned} \ln\left(e^{0.15h}\right) & = \ln\frac{3700}{1425} \\ \\ 0.15h & = \ln\frac{3700}{1425} \\ \\ h &= \frac{\ln\dfrac{3700}{1425}}{0.15} \\ \\ & \approx 6.4\text{ hours} \end{aligned}[/tex]
In conclusion, it will take about 6.4 hours for the population of the bacteria to reach 3700.
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