Question

Determine if the equation y=2.5(0.8)^x represents exponential growth growth or decay.
1.Exponential growth
2. Exponential decay

Answer 1

Exponential decay. How do you know?

Well, look at the formula. y = a(b)^x. If 0<b<1, then it is decay, and if b>1, it is growth. And if b=1, then it is a linear equation, because b^1 = b. Check it out--substitute values of x into this equation. For x = 0, the y-value is 2.5 because b^0 = 1. For x = 1, the y-value is 2. It keeps on decreasing, quicker and quicker.

Next time, just substitute increasing x-values into the equation, e.g. 0, 1, 2, 3, etc. If the y-value decreases the bigger x gets, it's decay. If the y-value increases the bigger x gets, it's growth.

Hope that helped. :)

Answer 2

Thanks.

Answer 3

You're welcome.