How do you determine if the equation #y = 1/3 (0.1)^x# represents exponential growth or decay?

Question

2022 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-03T11:21:10

See explanation.

An exponential function

#f(x)=axxb^x#

is:

a decreasing function (represents decay) if #a>0# and #b in (0;1)# or #a<0# and #b>1#
an increasng function (represents growth) if #a<0# and #b>1# or #a<0# and #b in (0;1)#

For the given function:

#a=1/3# and #b=0.1#, so #a>0# and #b in (0;1)#, therfore the function is decreasing (represents decay)