The size, S, of a tumor (in cubic millimeters) is given by S=2^t, where t is the number of months since the tumor was discovered. Give units with your answers.

(a) What is the total change in the size of the tumor during the first 9 months?

Answer: The total change is
and its units = .

(b) What is the average rate of change in the size of the tumor during the first 9 months?

Answer: The average rate of change is

,
and its units = .

(c) Use an interval of 0.001 to approximate the rate of change at which the tumor is growing at t=9.

Answer: The rate is

,

a) you just do 2^9 which is 512 cubic millimeters
b) using the average rate of change formula you get 56.78 cubic millimeters per month
c) I do not understand at all I am stuck on the same one

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MrRoyal MrRoyal · Answer 2 · 2022-02-18T12:36:14+01:00

The total change in size in the first 9 months is 512, and the average rate in the first 9 months is 56.89

The function is given as:

[tex]S = 2^t[/tex]

In the first 9 months, the total change in size is calculated as:

[tex]S = 2^9[/tex]

This gives

S = 512

The average rate in the first 9 months is then calculated as:

[tex]S' = \frac{S(9)}{9}[/tex]

Substitute 512 for 2^9

[tex]S' = \frac{512}{9}[/tex]

Evaluate

S' = 56.89