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

1 Answer
Jul 6, 2017

If b in #a(b)^x# is larger than 1.


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.