Question

Which of the following options results in a graph that shows exponential growth? f(x) = 0.4(3)^x f(x) = 3(0.5)^x f(x) = 0.8(0.9)^x f(x) = 0.9(5)^−x

Answer 1

See below

Explanation:

Let;s look at all the functions.

`f(x)=1.2^x`

graph{1.2^x [-10, 10, -5, 5]}

`f(x)=1.5^x`

graph{1.5^x [-10, 10, -5, 5]}

`f(x)=0.72^x`

graph{.72^x [-10, 10, -5, 5]}

`f(x=4.5^-x)`

graph{4.5^-x [-10, 10, -5, 5]}

The first two functions exhibit exponential growth. The last 2 functions show exponential decay.

The second function is closer to "true" exponential growth. `e` is a number equal to approximately `2.7`.

`y=e^x`

graph{e^x [-10, 10, -5, 5]}