How do you determine if the equation #y=0.5(1.2)^x # represents exponential growth or decay?

Question

4882 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-21T13:15:23

See explanation.

An exponential equation #f(x)=a*b^x# is a decreasing function (represents decay) if:

#a>0# and #bin(0;1)#

or

#a<0# and #b>1#

It is an increasing function (represents growth) if

#a<0# and #b in (0;1)#

or

#a>0# and #b>1#

In the given example #a=0.5# (so #a>0#) and #b=1.2# (so #b>1#).

If we look at the above explanation we can say that #f(x)# is an increasing function (represents growth)