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

1 Answer
May 3, 2017

See explanation.

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)