Question

The equation ​ yˆ=−6.2x2+51.5x+10.2 ​ approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 6:30 p.m.?

Answer 1

Notice that form 3 pm to 6:30 pm 3.5 hours have passed.
Since the function
`y=-6 x^(2) +51.5x+10.2` represent the average number of cars that pass through an intersection x hours after 3:00 p.m, we are going to replace
`x` with 3.5 to find the average number of cars that pass through the intersection at 6:30 p.m

`y=-6 x^(2) +51.5x+10.2`

`y=-6 (3.5)^(2) +51.5(3.5)+10.2`

`y=-6(12.25)+180.25+10.2`

`y=-73.5+190.45`

`y=116.95`

We can conclude that the average number of cars that pass through an intersection at 6:30 pm is approximately 117.

Answer 2

115 cars.

Explanation:

We have been given an equation
`y=-6.2x^2+51.5x+10.2` which approximates the average number of cars that pass through an intersection x hours after 3:00 p.m.

Since we know that there will be 3.5 hours between 3:00 pm and 6:30 pm. So to find the average number of cars that pass through the intersection at 6:30 pm we will substitute
`x=3.5` in our given equation.

`y=-6.2(3.5)^2+51.5(3.5)+10.2`

`y=-6.2*12.25+180.25+10.2`

`y=-75.95+180.25+10.2`

`y=114.5\approx 115`

Therefore, approximately 115 cars will passe through the intersection at 6:30 pm.