Question

question 10 of 10
the number of cases of a new disease can be modeled by the quadratic regression equation ( y = - 2 x ^ { 2 } + 44 x + 8 ), where ( x ) represents the year.
which is the best prediction for the number of new cases in year 20?
a. 88
b. 618
c. 422
d. 234

Explanation:

Step1: Substitute \(x = 20\) into the equation

Given \(y=-2x^{2}+44x + 8\), substitute \(x = 20\).

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Step2: Calculate \(x^{2}\) term

Calculate \((20)^{2}=400\). Then \(-2\times(20)^{2}=-2\times400=-800\).

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Step3: Calculate \(44x\) term

Calculate \(44\times20 = 880\).

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Step4: Calculate the sum

First, \(-800 + 880=80\), then \(80+8 = 88\).

Answer:

A. 88