Question

Which of the following options results in a graph that shows exponential growth?

f(x) = 0.4(0.2)x
f(x) = 4(0.98)x
f(x) = 0.7(5)x
f(x) = 5(4)−x

Answer 1

To determine which of the given options results in a graph that shows exponential growth, we need to identify functions where the base of the exponential term (the value being raised to the x) is greater than 1.

Let's analyze each function:

1. **f(x) = 0.4(0.2)^x**: The base is 0.2, which is less than 1. This results in exponential decay.

2. **f(x) = 4(0.98)^x**: The base is 0.98, which is also less than 1. This too results in exponential decay.

3. **f(x) = 0.7(5)^x**: Here, the base is 5, which is greater than 1. This indicates exponential growth.

4. **f(x) = 5(4)−x**: This can be rewritten as \( f(x) = 5(1/4)^x = 5(4^{-x}) \). The base \( 1/4 \) is less than 1, so this results in exponential decay as well.

Based on this analysis, the only function that results in exponential growth is:

**f(x) = 0.7(5)^x**.