in a lab experiment, 520 bacteria are placed in a petri dish. the conditions are such that the number of…

Explanation:

Step1: Define exponential growth formula

The formula for doubling growth is $N(t) = N_0 \times 2^{\frac{t}{d}}$, where $N(t)=2590$, $N_0=520$, $d=5$ hours, $t$ is time to find.

Step2: Isolate the exponential term

Divide both sides by $N_0$: $\frac{2590}{520} = 2^{\frac{t}{5}}$ Simplify left side: $\frac{259}{52} \approx 4.9808 = 2^{\frac{t}{5}}$

Step3: Take log of both sides

Use natural logarithm: $\ln(4.9808) = \frac{t}{5} \times \ln(2)$

Step4: Solve for t

Rearrange to solve for $t$: $t = 5 \times \frac{\ln(4.9808)}{\ln(2)}$ Calculate values: $\ln(4.9808)\approx1.605$, $\ln(2)\approx0.6931$ $t = 5 \times \frac{1.605}{0.6931} \approx 5 \times 2.316 \approx 11.6$

Answer:

11.6