Chapter 4.3, Problem 44E

Height of a Plant Let $f(t)$ be the function from Exercise 39 that gives the height (inches) of a plant at time $t$

(weeks ).

a. When is the plant $11$ inches tall ?

b. When is the plant growing at the rate of $1$ inch per week ?

c. What is the fastest rate of growth of the plant, and when does this occur?

Exercise 39. Heights of a Plant The height of a certain plant, in inches, after $t$ weeks is

$f\left(x\right)=\frac{1}{.05+e^{-0.4t}}$.

The graph of $f(t)$ resembles the graph in Fig. 3. Calculate the rate of growth of the plant after $7$ weeks.