How do you determine if the equation y=0.25(1.03)^5 represents exponential growth or decay?

Jul 6, 2017

If b in $a {\left(b\right)}^{x}$ is larger than 1.

Explanation:

In general, assuming if the exponent is positive, as long as the inner number is greater than 1, it will grow exponentially. To put this differently:

Assume an exponential function $a {\left(b\right)}^{x}$. Regardless of what a is as long as it does not equal 0 or negative if you're looking for positive growth, as long as $b > 1$ the function will grow.

In the case of $y = 0.25 {\left(1.03\right)}^{t}$, since b, which is 1.03, is larger than 1, it will grow exponentially.

I am assuming in this case that 5 is a placeholder for x or whatever variable it is supposed to represent.