THE FUNCTION D(X) MODELS THE CUMULATIVE NUMBER OF DEATHS FROM A DISEASE X YEARS AFTER 1984. ESTIMATE THE YEAR WHEN THERE WERE 90,000 DEATHS
D(x)=2010X^2+5400X+5774
Well, we could solve the quadratic but it says estimate.
make a guess at say ten years
d(10) = 201,000 + 54,000 + 5,774 way too big
d(5) = 50,250 + 27,000 + 5774 = 83,024
d(6) = 110,534
so between five and six years after 1984
So 1989
To estimate the year when there were 90,000 deaths, you need to solve the equation:
90,000 = 2010X^2 + 5400X + 5774
To solve this quadratic equation, you can use the quadratic formula:
X = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2010, b = 5400, and c = 5774. Plug in these values into the formula to find the values of X.
X = (-5400 ± √(5400^2 - 4 * 2010 * 5774)) / (2 * 2010)
Simplify the equation:
X = (-5400 ± √(29160000 - 46546240)) / 4020
X = (-5400 ± √(-17386240)) / 4020
Since the number inside the square root is negative, it means that there are no real solutions to this equation. This indicates that there is no value of X that would result in 90,000 deaths according to the given model.
Therefore, based on the given model, it is not possible to estimate the year when there were 90,000 deaths.