Out of a group of (50,000) births, the number of people, f(x), surviving to age (x) is modeled by the function f(x)=5000 square root 100-x. To what age will (20,000) people in the group survive?
To find the age at which 20,000 people in the group will survive, we need to solve the equation f(x) = 20,000. The given function f(x) = 5000 * √(100 - x) represents the number of people who survive to age x in a group of 50,000 births.
Now let's set up the equation:
20,000 = 5000 * √(100 - x)
To solve this equation for x, we need to isolate the square root term and then square both sides of the equation. Here are the steps:
1. Divide both sides of the equation by 5000:
(20,000 / 5000) = √(100 - x)
Simplifying, we have:
4 = √(100 - x)
2. Square both sides of the equation to get rid of the square root:
(4)^2 = (√(100 - x))^2
16 = 100 - x
3. Move the constant term to the other side of the equation:
100 - 16 = x
84 = x
Therefore, 20,000 people in the group will survive until age 84.