Question

The function y=-x^2+65x+256 models the number y of subscribers to a website, where x is the number of days since the website launched. The number of subscribers to a competitor's website can be modeled by a linear function. The websites have the same number of subscribers on Days 1 and 34. a. Write a linear function that models the number of subscribers to the competitor's website.

Answer 1

Answer:

$y = 30x+290$

Step-by-step explanation:

Given

$y=-x^2+65x+256$

Required

The linear function of a competitor's website

On day 1, both websites have the same subscribers.

This implies that:

$y=-x^2+65x+256$

Substitute: $x =1$

$y=-(1)^2+65*1+256$

$y=-1+65+256$

$y=320$

This implies:

$(x_1,y_1) = (1,320)$

On day 34, both websites have the same subscribers.

This implies that:

$y=-x^2+65x+256$

Substitute: $x =34$

$y=-(34)^2+65*34+256$

$y=-1156+2210+256$

$y=1310$

This implies:

$(x_2,y_2) = (34,1310)$

To calculate the linear function of the competitor, we have:

$(x_1,y_1) = (1,320)$

$(x_2,y_2) = (34,1310)$

Calculate slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{1310 - 320}{34-1}$

$m = \frac{990}{33}$

$m = 30$

The equation is then calculated as:

$y = m(x - x_1) + y_1$

This gives:

$y = 30 * (x - 1) + 320$

Open bracket

$y = 30x - 30 + 320$

$y = 30x+290$ --- This represents the linear function of the competitor's website