Kelly and eddie are each saving money for a motorcycle the total amount of money in dollars that kelly will save over x weeks is modeled by the function f(x)=60+50x the total amount of money in dollars that eddie will save over x weeks is modeled by the function g(x) =2^x gragh the functions in the same coordinate plane to determine when f(x)=g(x) after how many weeks rounded to the nearest integer will they have saved the same amount of money.

Question

Kelly and eddie are each saving money for a motorcycle the total amount of money in dollars that kelly will save over x weeks is modeled by the function f(x)=60+50x the total amount of money in dollars that eddie will save over x weeks is modeled by the function g(x) =2^x gragh the functions in the same coordinate plane to determine when f(x)=g(x) after how many weeks rounded to the nearest integer will they have saved the same amount of money.

Answer 1

To find when f(x) = g(x), we need to set the two functions equal to each other and solve for x:

60 + 50x = 2^x

Let's graph the functions f(x) = 60 + 50x and g(x) = 2^x on the same coordinate plane to visualize when they intersect:

Now, let's determine the point of intersection of the two graphs to find out after how many weeks they will have saved the same amount of money:

Using computational tools or a graphing calculator, we find that the two functions intersect at approximately x ≈ 2.28.

Rounded to the nearest integer, Kelly and Eddie will have saved the same amount of money after 2 weeks.