Answer:
A sample of 16577 is required.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the z-score that has a p-value of
.
The margin of error is of:

99% confidence level
So
, z is the value of Z that has a p-value of
, so
.
She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?
We have no estimation for the proportion, and thus we use
, which is when the largest sample size will be needed.
The sample size is n for which M = 0.01. So






Rounding up:
A sample of 16577 is required.
The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: 
Given that:


Let the number of months be t. So, the function C(t) is calculated as follows:



The range is calculated as follows:
The smallest possible value of t is 0 i.e. when no monthly subscription is done.
So, we have:

And the highest is
i.e. for a large value of t
So, we have:

Hence, the range of the function is:

Read more about range of functions at:
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