Question

A local water park found that if the price of admission was $16, the attendance was about 2850 customers per week. When the price of admission was dropped to $10attendance increased to about 3100 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp + b)

Answer 1

1) Gathering the data

$16 price of admission

2850 customers per week.

$10 price of admission

3100 per week.

A = Attendance

m=

p=price

b=

2) Since this is a linear equation (y=mx+b) we can identify those figures as points (16, 2850) and (10, 3100).

Let's find the slope m

2.2) Let's find the linear coefficient "b", the point where the line intercepts the y-axis, by plugging one of those points, usually the simpler one: (10,3100)

y=mx +b In this case

A =mp +b

3100 = -125/3(10) +b

3100 = -1250/3 +b

10550/3=b or b =3516.67

3) So finally, the Attendance in that local water park follows this function:

`A=(-125)/(3)x+(10550)/(3)`