Explain how you can tell the difference between exponential growth and exponential decay by looking at a function rule.

Growth and Decay examples down below!

Step-by-step explanation:

Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

Exponential growth (decay) is a way of describing the growth (decay) of a certain variable x (money, population, mass, etc..) with respect to time.

It happens when the speed of growth (decay) is proportional to the quantity itself at any given instant t.

If x(t) is the amount of the variable x at a certain instant t, the exponential growth (decay) can be modeled with the equation

where C is the initial amount of x (when t=0) and it's always considered positive, and b, r are constants that depend on the speed of growth (decay).

To find out if x(t) represents exponential growth, check b and r.

If b > 1 AND r > 0 then x(t) represents an exponential growth.

If r < 0 AND b >1  OR r > 0 AND 0 < b < 1 then it is an exponential decay.