Question

How do you determine if the equation `y = 0.84(1.45)^x` represents exponential growth or decay?

Answer 1

Look at the number in front of x: If it is less that 1, the graph slopes downwards, if it is greater than 1 the graph slopes upwards.

Explanation:

Look at the number in front of x:

If it is less that 1, the graph slopes downwards:
graph{0.5^x [-10, 10, -5, 5]}
If it is greater than 1 the graph slopes upwards:
graph{1.5^x [-10, 10, -5, 5]}

Since y=0.84(1.45) is greater than 1, we know it is growing.
graph{0.84(1.45)^x [-10, 10, -5, 5]}