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]?

The average rate of change is

Step-by-step explanation:

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

Where, t represents the number of weeks.

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

From equation (1),

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: