How do you determine if the equation #y = (0.3)^x # represents exponential growth or decay?

1 Answer
Gió
Jul 26, 2015

Explanation:

You have:
#y=0.3^x#
that can be written as:
#y=(3/10)^x# in this way you can see that
1] When #x<0# the value of your function gets smaller and smaller for #x->0#; consider for example:
#x=-2# then #y=(3/10)^-2=(10/3)^2=11.1#
#x=-1# then #y=(3/10)^-1=(10/3)^1=3.3#
2] the denominator, #10#, is always bigger (when #x>0#) than the numerator reducing the value of your fraction every time you increase the value of #x# of the exponent.
Graphically:
graph{(0.3)^x [-12.66, 12.65, -6.33, 6.33]}

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