How do you determine if #y=0.2(5)^-x# is an exponential growth or decay?

1 Answer
Jan 17, 2017

This is exponential decay. Two ways to tell are discussed below...

Explanation:

First, the negative exponent is an indicator of decay. You could rewrite the expression (without a negative exponent) as

#y=0.2/5^x#

This helps you to see that as #x# gets very large, the expression gets very small - clearly not a case of growth.

Alternatively, you could make a chart in which you test increasing values of #x#, starting at #x=1# (for example) and increasing slowly to #x=5#. You would see the results - the expression would decrease in value rapidly.