Determine whether 5(1.2 ) x represents exponential growth or decay. Explain.

Answer 1

Mare:

I assume we are talking about y = 5*(1.2)^x

For a function of type a*b^x , where a>0, if b<1 we have exponential decay; if b>1 we have exponential growth.

For y = 5*(1.2)^x, a = 5 > 0 and b = 1.2 > 1. Do we have exponential growth or decay?

Answer 2

Whenever the base of a power is greater than one, exponential growth occurs as x increases. One way to see this is that if I increase x by one, I'm multiplying the previous number by a number greater than one, so that it increases.

Example: y(1) = 5(1.2)^1 = 5*1.2,

y(2) = 5(1.2)^2 = (5*1.2)*1.2.