Work Step by Step
a) The meaning the the derivative is the rate (bacteria per hour) at which the number of bacteria is changing (growing) in the controlled laboratory at t=5hrs. b) We would assume that $f'(10)$ is larger because bacteria grow at an exponential rate when they have unlimited space and nutrients. Therefore, the rate at which the number of bacteria is growing would become higher as the population increases. If nutrients were limited, the opposite may be true. If there is not enough food to support the number of bacteria in the tank after 10 hours, it is possible that $f'(5)$ could be larger than $f'(10)$.