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

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:

$\frac{98}{1000}$

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 ${\left(\frac{98}{1000}\right)}^{t}$ 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!