a scientist writes the equation $n(h)=100e^{0.25h}$ to model the growth of a certain bacteria in a petri…

Explanation:

Step1: Set up the equation

We are given $N(h)=100e^{0.25h}$ and $N = 450$. So, $450=100e^{0.25h}$.

Step2: Isolate the exponential term

Divide both sides by 100: $\frac{450}{100}=e^{0.25h}$, which simplifies to $4.5 = e^{0.25h}$.

Step3: Take the natural - logarithm of both sides

$\ln(4.5)=\ln(e^{0.25h})$. Since $\ln(e^{x}) = x$, we have $\ln(4.5)=0.25h$.

Step4: Solve for h

$h=\frac{\ln(4.5)}{0.25}$. We know that $\ln(4.5)\approx1.5041$, so $h=\frac{1.5041}{0.25}=6.0164\approx6$.

Answer:

6 hours