1984-1994 the equation the number of aids cases can be modeled by the equation
C(x)=3034x^2+14,018x+6400
X represents years after 1984 estimate the year when 200,000 aids cases had been diagnosed.
done when you posted this earlier.
To estimate the year when 200,000 AIDS cases had been diagnosed, we can set the equation C(x) = 200,000 and solve for x.
C(x) = 3034x^2 + 14,018x + 6400
200,000 = 3034x^2 + 14,018x + 6400
Now, we need to solve this quadratic equation. Let's rearrange it to standard form:
3034x^2 + 14,018x + 6400 - 200,000 = 0
3034x^2 + 14,018x - 193,600 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3034, b = 14,018, and c = -193,600.
x = (-14,018 ± √((14,018)^2 - 4(3034)(-193,600))) / (2(3034))
Calculating this gives us:
x = (-14,018 ± √(196,603,524 + 2,217,536,640)) / 6068
x = (-14,018 ± √(2,414,140,164)) / 6068
x = (-14,018 ± 49,136.67) / 6068
Now we can find two possible values for x:
x1 = (-14,018 + 49,136.67) / 6068
x1 = 3.86
x2 = (-14,018 - 49,136.67) / 6068
x2 = -10.35
Since x represents years after 1984, we can disregard the negative value for x.
Therefore, the estimate for the year when 200,000 AIDS cases had been diagnosed is approximately 1984 + 3.86 = 1987.86.
This means that it is estimated that around 200,000 AIDS cases had been diagnosed in the year 1987 or early 1988.
To estimate the year when 200,000 AIDS cases had been diagnosed, you need to find the value of x that satisfies the equation C(x) = 200,000.
The equation C(x) = 3034x^2 + 14,018x + 6400 represents the number of AIDS cases at a given year (x) after 1984. So, substituting 200,000 for C(x) in the equation, we get:
200,000 = 3034x^2 + 14,018x + 6400
Now, you need to solve this quadratic equation for x to find the estimated number of years after 1984 when 200,000 AIDS cases had been diagnosed. You can use various methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
In this case, you can solve this quadratic equation by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 200,000 = 3034x^2 + 14,018x + 6400, the coefficients are:
a = 3034
b = 14,018
c = 6400
Plugging these values into the quadratic formula, we get:
x = (-14,018 ± √((14,018)^2 - 4 * 3034 * 6400)) / (2 * 3034)
By solving this equation, you will obtain two possible values for x (positive and negative). The positive value will represent the time after 1984 when the AIDS cases reach 200,000.
I'll calculate the solution for you: