Question

The population, y, of a small town can be represented using a quadratic model. The maximum population, 6,000 people, occurred 20 years after record keeping began. Five years later, the population was 5,950. If x represents the number of years after record keeping began, which equation represents the given scenario? y = 2(x – 20)2 + 6,000 y = –2/9(x – 20)2 + 6,000 y = –2(x – 20)2 + 6,000 y =2/9 (x – 20)2 + 6,000

Answer 1

Answer:

y = -2(x - 20)² + 6000

Step-by-step explanation:

Given: The maximum population, 6,000 people, occurred 20 years after record keeping began. Five years later, the population was 5,950

To Find: If x represents the number of years after record keeping began, which equation represents the given scenario?

Solution:

Vertex = (20,6000) and the parabola opens downward.  

So, Equation is:  

y = A (x - 20)² + 6000    --1

Now, we need to find A.

It is also given that Five years later, the population was 5,950

This means in 25th year the population was 5950.

So, point (25,5950) is on the parabola. Now substitute the given point in the equation to get value of A

5950 = A (25 - 20)² + 6000  

-50 = A (5)²  

-50 = 25 A  

A = -2  

Now substitute the value of A in 1

Thus Equation becomes:   y = -2(x - 20)² + 6000

Hence Option 3 is correct .

y = -2(x - 20)² + 6000 represent the situation.

Answer 2

Y = –2(x – 20)^2 + 6,000

Hope This Is Sufficient !!