Nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f (x) = 36 + 4x. the total amount of money adam will save is given by the function g (x) = x2 + 15. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

For this case we have the following functions:

f (x) = 36 + 4x

g (x) = x2 + 15

By matching both functions we have:

f (x) = g (x)

36 + 4x = x2 + 15

Rewriting we have:

x2 + 15 - 4x - 36 = 0

x2 - 4x - 21 = 0

Solving the polynomial we have:

(x-7) (x + 3) = 0

x = - 3

x = 7

Taking the positive root we have:

x = 7

Answer:

They will have the same amount of money saved after:

x = 7 weeks