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

`f(x) = 0.4(3)^x`

Explanation:

Remember that for a function to be exponential you need the number to which is being elevated to a certain exponent to be greater than 1, since in the options the only one that is greater than 1 is (3) the first option is the only one that is actually exponential eventhough all of them have exponents.

Answer 2

f(x) = 0.4·3^x

Explanation:

Exponential growth occurs when the base is greater than 1 and the exponent is an increasing non-negative function of the variable, or when the problem can be cast in that form using the rules of exponents.

Here, in f(x) = 0.4×3^x, the base is 3 (greater than 1), and the exponent of x has a positive coefficient.