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Sagot :
Answer:
[tex]y = 30x+290[/tex]
Step-by-step explanation:
Given
[tex]y=-x^2+65x+256[/tex]
Required
The linear function of a competitor's website
On day 1, both websites have the same subscribers.
This implies that:
[tex]y=-x^2+65x+256[/tex]
Substitute: [tex]x =1[/tex]
[tex]y=-(1)^2+65*1+256[/tex]
[tex]y=-1+65+256[/tex]
[tex]y=320[/tex]
This implies:
[tex](x_1,y_1) = (1,320)[/tex]
On day 34, both websites have the same subscribers.
This implies that:
[tex]y=-x^2+65x+256[/tex]
Substitute: [tex]x =34[/tex]
[tex]y=-(34)^2+65*34+256[/tex]
[tex]y=-1156+2210+256[/tex]
[tex]y=1310[/tex]
This implies:
[tex](x_2,y_2) = (34,1310)[/tex]
To calculate the linear function of the competitor, we have:
[tex](x_1,y_1) = (1,320)[/tex]
[tex](x_2,y_2) = (34,1310)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{1310 - 320}{34-1}[/tex]
[tex]m = \frac{990}{33}[/tex]
[tex]m = 30[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 30 * (x - 1) + 320[/tex]
Open bracket
[tex]y = 30x - 30 + 320[/tex]
[tex]y = 30x+290[/tex] --- This represents the linear function of the competitor's website
The linear function of the competitor's website is represented by y=30x-290.
We have given that,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.
We have to find the linear function of a competitor's website.
For the day 1, both websites have the same subscribers.
This implies that
[tex]y=-x^2+65x+256[/tex]
x represent the value of day
so plug x=1 we get
[tex]y=(-1)^2+65+256[/tex]
[tex]y=-1+65+256\\y=320[/tex]
Therefore we get the point
[tex](x_1,y_1)=(1,320)[/tex]
On day 34, both websites have the same subscribers.
[tex]y=-x^2+65x+256[/tex]
x=34
[tex]y=-(34)^2+65\times 34+256[/tex]
[tex]y=-1156+2210+256\\y=1310[/tex]
[tex](x_2,y_2)=(34,1310)[/tex]
What is the slope point form?
[tex](y_2-y_1)=m(x_2-x_1)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{1310-320}{34-1} \\m=\frac{990}{33} \\m=30[/tex]
Now slope point form is
[tex]y-y_1=m(x-x_1)[/tex]
Theefore we get
[tex]y=30(x-1)+320[/tex]
[tex]y=30x-290[/tex]
Therefore, the linear function of the competitor's website is represented by y=30x-290.
To learn more about the linear model visit:
https://brainly.com/question/25987747
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