Question

When writing an equation in exponential form , how can you tell by the number in parentheses if it's exponential growth or exponential decay?

Answer 1

One example of a growth is saving rate, let's say that the increase is 4% per annum

The multiplier is 100%+4%=104% = 1.04

The growth formula is
y = A₀(1.04)ˣ
Where A₀ is the initial value

One example of a decay is a decrease of 12% per annum

The multiplier is 100% - 12% = 78% = 0.78

The equation for the decay is
y = A₀(0.75)ˣ

The difference between these two equations is that for the growth, we have a multiplier that is bigger than 1, whereas, for the decay, we have a multiplier that is less than 1.