The number of bacteria \( P(h) \) in a certain population increases according to the following function, where time \( h \) is measured in hours. \[ P(h)=2600 e^{0.06 h} \] How many hours will it take for the number of bacteria to reach 3200 ? Round your answer to the nearest tenth, and do not round any intermediate computations.

To find out how many hours it will take for the number of bacteria to reach 3200, we need to solve the equation: \[ 3200 = 2600 e^{0.06 h} \] First, we can divide both sides by 2600 to isolate the exponential function: \[ \frac{3200}{2600} = e^{0.06 h} \] Calculating this gives: \[ 1.230769 = e^{0.06 h} \] Next, we take the natural logarithm (ln) of both sides: \[ \ln(1.230769) = 0.06 h \] Calculating the natural logarithm: \[ \ln(1.230769) \approx 0.20899 \] Now, we can solve for \( h \): \[ h = \frac{0.20899}{0.06} \] Calculating this gives: \[ h \approx 3.48 \] Rounding to the nearest tenth, it will take approximately \( 3.5 \) hours for the number of bacteria to reach 3200.