Question

Here are equations defining three exponential functions f,g, and h.f(x)=100×3^x, g(x)=100×(3.5)^x, h(x)=100×4^xWhich of these functions grows the least quickly? Which one grows the most quickly?

Answer 1

Given:

`\begin{gathered} f\mleft(x\mright)=100*3^x \\ g\mleft(x\mright)=100*\mleft(3.5\mright)^x \\ h\mleft(x\mright)=100*4^x \end{gathered}`

To find the function which has the least and most quickly grows:

Since 3 < 3.5 < 4.

So, the function that has the most quickly grows is,

`h(x)=100*4^x`

So, the function that has the least quickly grows is,

`f(x)=100*3^x`