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?

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20-12-2022
Mathematics

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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?

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-23T02:50:25-05:00

y = -25x^2 + 600x + 4000 is equation represents the given scenario.

We can use the two given points, (20, 6000) and (25, 5950) to find the equation of the quadratic. First, we need to calculate the slope. In this case, the slope is (6000-5950)/(20-25), or -50.

We may now find the equation by using the line's point-slope form.The point-slope form is y - y1 = m(x - x1). Substituting our values, we get y - 6000 = -50(x - 20). Simplifying and solving for y, we get y = -50x + 6000.

Next, we need to convert this linear equation into a quadratic equation. To do this, we need to multiply both sides of the equation by x. This gives us yx = -50x^2 + 6000x. Rearranging the terms, we get y = -50x^2 + 6000x. Finally, we need to add 4000 to both sides to get y = -50x^2 + 6000x + 4000.

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