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Sagot :
The model provided in the question is given to be:
[tex]P(t)=375e^{0.19t}[/tex]Double the bacteria population is:
[tex]\Rightarrow375\times2=750[/tex]To find the time taken to get that population, we will equate P(t) to 750. Therefore,
[tex]750=375e^{0.19t}[/tex]We can solve this using the following steps.
Step 1: Divide both sides by 375
[tex]\begin{gathered} \frac{750}{375}=\frac{375e^{0.19t}}{375} \\ 2=e^{0.19t} \\ \Rightarrow e^{0.19t}=2 \end{gathered}[/tex]Step 2: Find the natural logarithm of both sides
[tex]\ln e^{0.19t}=\ln 2[/tex]Step 3: Recall that the product of the natural logarithm and the natural exponent is the same. Hence, we have
[tex]0.19t=\ln 2[/tex]Step 4: Divide both sides by 0.19
[tex]\begin{gathered} \frac{0.19t}{0.19}=\frac{\ln 2}{0.19} \\ t=\frac{\ln 2}{0.19} \end{gathered}[/tex]Step 5: Evaluate the answer using a calculator
[tex]t=3.6\approx4[/tex]ANSWER
It takes 4 minutes for the bacteria to double its population.
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