Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 46

Suppose that the function $n=f(t)$ represents the number of bacteria after $t$ hours in a laboratory experiment.



a.) State the meaning of the derivative $f'(5)$ and its corresponding units.



b.) If there is an unlimited amount of space and nutrients of the bacteria, which do you think is
larger, $f'(5)$ or $f'(10)$? If the supply of nutrient is limited, would that affect your conclusion? Explain.






$\quad$ a.) $f'(5)$ means the rate how fast the number of bacteria is changing in 5 hours; its unit is $\displaystyle \frac{\text{bacteria}}{\text{hours}}$



$\quad$ b.) For unlimited amount of space and nutrients, $f(10)>f(5)$ since the growth only depends
on the population at a certain time. If the supply is insufficient, the population may be depleted
causing the growth rate to decrease