Question

The number of cases of a new disease can be modeled by the quadratic regression equation y = –2x^2 + 44x + 8, where x represents the year. Which is the best prediction for the number of new cases in year 20?

a. 234
b. 422
c. 618
d. 88

Answer 1

To predict the number of new cases in year 20 using the quadratic regression equation y = -2x^2 + 44x + 8, we need to substitute x = 20 into the equation and solve for y.

Let's calculate:

y = -2(20)^2 + 44(20) + 8

y = -2(400) + 880 + 8

y = -800 + 880 + 8

y = 88

Therefore, the best prediction for the number of new cases in year 20 is 88. So, the correct option is d. 88.

Answer 2

Option d is correct

88 is the best prediction for the number of new cases in year 20

Explanation:

The number of cases of a new disease can be modeled by the quadratic regression equation :

`y = -2x^2+44x+8` .....[1]

where, x represents the year.

We have to find the best prediction for the number of new cases in year 20.

Substitute x = 20 years in [1] we have;

`y = -2(20)^2+44(20)+8 = -800+880+8 = 80+8 = 88`

Therefore, 88 is the best prediction for the number of new cases in year 20