Question

The number of visitors to an indoor water park in a month can be modeled by g(x)=15000(0.98)^x, where x is the number of months since the water park opened. Describe the dilation in g(x) as it relates to the parent function f(x)=0.98^x.

Answer 1

the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 15000.

Explanation:

The function g(x) is a dilation of the parent function f(x) = 0.98^x.

Specifically, g(x) = 15000(0.98)^x is a vertical dilation of f(x) = 0.98^x by a factor of 15000.

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 15000.

In other words, the values of g(x) are 15000 times greater than the values of f(x) for any given value of x.

For example, when x = 1, f(1) = 0.98 and g(1) = 15000(0.98) = 14700. This means that the number of visitors to the water park in the second month (x = 1) is 15000 times greater than the number of visitors in the first month.

Overall, the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 15000.