The number of bacteria \( P(h) \) in a certain population increases according to the following function, where time \( h \) is measured in hours. \[ P(h)=2200 e^{0.16 h} \] How many hours will it take for the number of bacteria to reach 2900 ? Round your answer to the nearest tenth, and do not round any intermediate computations.

Given the equation \[ 2200 e^{0.16h} = 2900, \] we start by isolating the exponential term. Divide both sides by 2200: \[ e^{0.16h} = \frac{2900}{2200}. \] Taking the natural logarithm on both sides gives: \[ \ln\left(e^{0.16h}\right) = \ln\left(\frac{2900}{2200}\right). \] Using the logarithm property \( \ln(e^x) = x \), we have: \[ 0.16h = \ln\left(\frac{2900}{2200}\right). \] Now, solve for \( h \): \[ h = \frac{\ln\left(\frac{2900}{2200}\right)}{0.16}. \] Using a calculator for the intermediate computation: \[ \frac{2900}{2200} \approx 1.31818, \] \[ \ln(1.31818) \approx 0.276, \] \[ h \approx \frac{0.276}{0.16} \approx 1.725. \] Rounded to the nearest tenth, it will take approximately \( \mathbf{1.7} \) hours for the number of bacteria to reach 2900.