The number of bacteria, $B(h)$, in a certain population increases according to the following function, where time, $h$, is measured in hours: \[ B(h)=1425 e^{0.15 h} \] How many hours will it take for the bacteria to reach 3600 ? Round your answer to the nearest tenth, and do not round any intermediate computations.

Step 1 ：We are given the function \(B(h)=1425 e^{0.15 h}\) and we want to find the time \(h\) it takes for the bacteria population to reach 3600. This means we need to solve the equation \(1425 e^{0.15 h} = 3600\) for \(h\).

Step 2 ：First, we divide both sides of the equation by 1425 to isolate the exponential term: \(e^{0.15 h} = \frac{3600}{1425}\).

Step 3 ：Next, we take the natural logarithm of both sides to solve for \(h\): \(0.15 h = \ln\left(\frac{3600}{1425}\right)\).

Step 4 ：Finally, we divide both sides by 0.15 to solve for \(h\): \(h = \frac{\ln\left(\frac{3600}{1425}\right)}{0.15}\).

Step 5 ：By calculating the above expression, we find that \(h \approx 6.2\).

Step 6 ：So, it will take approximately \(\boxed{6.2}\) hours for the bacteria population to reach 3600.