Question

Destiny invest $4000 in an account that earns 3.5% interest per years compound annually. The amount of money in her account after x years can be modeled by g(x)=4000(1.035)^x. Describe the dilation in g(x) as it relates to the parent function f(x)=1.035^x.

Answer 1

Explanation:

The function g(x) is a dilation of the parent function f(x) = 1.035^x.

Specifically, g(x) = 4000(1.035)^x is a vertical dilation of f(x) = 1.035^x by a factor of 4000.

This means that the graph of g(x) is the same shape as the graph of f(x), but it is vertically stretched by a factor of 4000.

In other words, the values of g(x) are 4000 times greater than the values of f(x) for any given value of x.

For example, when x = 1, f(1) = 1.035 and g(1) = 4000(1.035) = 4140. This means that the amount of money in Destiny's account after one year is 4000 times greater than the initial amount she invested.

Overall, the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 4000.