Chapter 2.5, Problem 70E

(a)

To determine

To calculate: The rate of change of N with respect to t, when $t=0$, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$.

(b)

To determine

To calculate: The rate of change of N with respect to t, when $t=1$, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$

(c)

To determine

To calculate: The rate of change of N with respect to t, when $t=2$, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$

(d)

To determine

To calculate: The rate of change of N with respect to t, when $t=3$, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$

(e)

To determine

To calculate: The rate of change of N with respect to t, when $t=4$, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$

(f)

To determine

The conclusion from the rate of change of N with respect to t for different values of t, where N is the number of bacteria in a culture after t days modeled by the equation $N=400\left[1-\frac{3}{{\left(t^2+2\right)}^2}\right]$