Question

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

Answer 1

If b in `a(b)^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(b)^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(1.03)^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.