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

Answer:

The average rate of change is $\frac{18}{5}$

Step-by-step explanation:

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

$P(t)=\frac{90t}{t+1}------(1)$

Where, t represents the number of weeks.

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

$m=\frac{P(24)-P(0)}{24-0}$

From equation (1),

$=\frac{\frac{90\times 24}{24+1}-\frac{90\times 0}{0+1}}{24}$

$=\frac{\frac{2160}{25}-\frac{0+1}{0}}{24}$

$=\frac{2160}{25\times 24}$

$=\frac{2160}{600}$

$=\frac{18}{5}$