Question

The population of a culture of cells grows according to the function P(t)= 90t/ t + 1, where t> or =0 is measured in weeks. Complete parts (a) and (b) below.

What is the average rate of change in the population over the interval [0,24]?

Answer 1

The average rate of change is
`(18)/(5)`

Explanation:

Given function that shows the population of a culture of cells,

`P(t)=(90t)/(t+1)------(1)`

Where, t represents the number of weeks.

Thus, the average rate of change in the population over the interval [0,24],

`m=(P(24)-P(0))/(24-0)`

From equation (1),

`=((90* 24)/(24+1)-(90* 0)/(0+1))/(24)`

`=((2160)/(25)-(0+1)/(0))/(24)`

`=(2160)/(25* 24)`

`=(2160)/(600)`

`=(18)/(5)`