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A local water park found that if the price of admission was $19, the attendance was about 1550 customers per week. When the price of admission was dropped to $16,attendance increased to about 2350 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp + b)

Sagot :

Given:

When the price of admission was $19, the attendance was about 1550 customers per week

And, when the price of admission was dropped to $16,

attendance increased to about 2350 per week

Let the attendance = A

And the price = p

The linear equation will be A = mp + b

Where (m) is the slope and (b) is the y-intercept

So,

When p = 19, A = 1550

When p = 16, A = 2350

So,

[tex]m=\frac{2350-1550}{16-19}=\frac{800}{-3}=-\frac{800}{3}[/tex]

So,

[tex]A=-\frac{800}{3}p+b[/tex]

we will find the value of (b) as follows:

[tex]\begin{gathered} 1550=-\frac{800}{3}\cdot19+b \\ 1550=-\frac{15200}{3}+b \\ b=\frac{19850}{3} \end{gathered}[/tex]

So, the answer will be the linear equation is:

[tex]A=\frac{-800}{3}p+\frac{19850}{3}[/tex]

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