Does the exponential function, y=(1.05)x, model exponential growth or exponential decay?

A.)Exponential growth because the base is less than 1.

B.)Exponential growth because the base is greater than 1.

C.)Exponential decay because the base is less than 1.

D.)Exponential decay because the base is greater than 1.

Respuesta :

Answer: B.)Exponential growth because the base is greater than 1.

Explanation:

The exponential function [tex]y = (1.05)^x[/tex] is the same as [tex]y = 1*(1.05)^x[/tex]

It's in the form [tex]y = a*b^x[/tex] where b = 1.05 is the base of the exponential. This value being larger than 1 will mean y increases along with x. So we have exponential growth. If [tex]0 < b < 1[/tex], then we'd have exponential decay.