Answer
The bacterial will reach 10, 000 after 6.11 hours
Step-by-step explanation:
Part B
[tex]\begin{gathered} Given\text{ that} \\ N(t)\text{ = 1500 }e^{0.31t} \\ \text{After how many hours will the number of bacteria reach 10, 000} \\ \text{let N(t) = 10, 000} \\ t\text{ = time in hours} \\ 10,000\text{ = 1500}e^{0.31t} \\ \text{Divide both sides by 1500} \\ \frac{10,000}{1,500}\text{ = }\frac{1500}{1500}e^{0.31t} \\ 6.666\text{ = }e^{0.31t} \\ \text{Take the natural logarithms of both sides} \\ \ln (6.666)\text{ = }\ln e^{0.31t} \\ \ln (6.666)\text{ = 0.31t} \\ 1.897\text{ = 0.31t} \\ \text{Divide both sides by 0.31} \\ \frac{1.897}{0.31}\text{ = }\frac{0.31t}{0.31} \\ t\text{ = 6.11 hours} \\ \text{Hence, the bacteria will reach 10, 000 after 6.11 hours} \end{gathered}[/tex]