How do you determine if the equation #y = (2)^x# represents exponential growth or decay?

2 Answers
Mar 26, 2018

When #x>1# it represents growth, when #x<1# it represents decay.

(When #x=1# it is a constant)

Mar 26, 2018

Answer:

Check the sign of the exponent, and you will find that it represents exponential growth.

Explanation:

As #x# increases in value, #y# increases as well, and will approach infinity with increasing #x#. This is because the equation is raising 2 to #+x#, indicating exponential growth (see below).

graph{2^x [-23.17, 56.83, -6.88, 33.12]}

If the equation was #y=2^(-x)# y would be in exponential decay, with #y# approaching 0 as #x# goes to infinity. Again, we can show this on a plot (see below).

graph{2^(-x) [-23.17, 56.83, -6.88, 33.12]}

Basically, the sign of the exponent tells you if the function is increasing or decreasing.