# It has been estimated that the number of people who will see a newspaper advertisement that has...

## Question:

It has been estimated that the number of people who will see a newspaper advertisement that has run for {eq}x {/eq} consecutive days is of the form {eq}N(x) = T - \frac{1}{2} \frac{T}{x} {/eq} for {eq}x \geq 1 {/eq}, where {eq}T {/eq} is the total readership of the newspaper.

If a newspaper has a circulation of 450,000, an ad that runs for {eq}x {/eq} days will be seen by {eq}N(x) = 450,000 - \frac{225,000}{x} {/eq} people.

Find how fast this number of potential customers is growing when this ad has run for 5 days.

_____ customers per day

## Rate of Change:

To find how fast or slow any given function is changing we will differentiate the function with respect to the given variable using the standard derivative formulas:

{eq}\frac{\mathrm{d} }{\mathrm{d} x}x^{n}=nx^{n-1}\\ {/eq}

$$N(x) = 450,000 - \frac{225,000}{x}$$

We will differentiate this function:

$$N'(x)=\frac{225000}{x^2}\\ N'(5)=9000$$

Customers per day.