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Yanka [14]
1 year ago
5

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 lau

nched. 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.
Mathematics
1 answer:
Wittaler [7]1 year ago
5 0

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

<em></em>y = 30x+290<em> --- This represents the linear function of the competitor's website</em>

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