Looking for Insight

Question

Hi, I was looking for insight on the breakdown of this equation if anyone could assist

In a certain population, there are 28,520 births on a particular day. The number, N, of these people surviving to age x can be modeled by the function        

                 N = 2850√(100-x).

1. using this model, how many (N) of the 28520 babies will survive to age 5?

2. What is the practical domain of this function?

3, When only 5,000 of this group are still alive, how old (x) do you expect them to be?

4. after how many years (x) will half the original population of 28,520 people (N=14,260) remain alive?

Answer 1

                 N = 2850√(100-x).

1. using this model, how many (N) of the 28520 babies will survive to age 5?

Substitute x = 5

2850*SQRT(100-5) = 27,778.4 = 27.778 babies (need to round to the nearest integer)

2. What is the practical domain of this function?

This is asking what values can x take on. The minimum value of anyone is x = 0 at birth

The maximum value of 100-x that keeps a non-negative value is x = 100.

The domain of x is [0,100]

3, When only 5,000 of this group are still alive, how old (x) do you expect them to be?

5000 = 2850 * SQRT(100-x)

(5000/2850)^2 = 100-x

x = 100 - (5000/2850)^2 = 97 years old

4. after how many years (x) will half the original population of 28,520 people (N=14,260) remain alive?

14260 = 2850 * SQRT(100-x)

x = 100 - (14260/2850)^2 = 25 years