How do you determine if the equation #y=39(0.098)^t# represents exponential growth or decay?

1 Answer
Aug 12, 2017

I would say decay.

Explanation:

We can have a look at the base #0.098# of your exponential. Written as it is it doesn't tell us much but what if we write it as:

#98/1000#

this is very good because we see that if you try to use your exponent #t# applied to this fraction you see that:

#98^t# becomes big BUT #1000^t# becomes bigger!!!

So, the fraction #(98/1000)^t# will become very small (the denominator is always bigger) when #t# increases!

Try with #t=1# and #t=2# you'll get:

#98^1/1000^1=0.098#

and:

#98^2/1000^2=0.0096#

So our exponential function will return us values that become smaller as #t# increases!

Graphically we see this as:
graph{39(0.098)^x [-11.25, 11.25, -5.625, 5.625]}

Hope it helps!