Without graphing, how can you determine if a function is an exponential growth or exponential decay function?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

An exponential function is of the general form f(t) = a*b^t

Here a = f(0) and b is a constant.

If b lies between 0 and 1, it is an exponential decay function.

On the other hand if b is greater than 1, it is an exponential growth function.

For example f(t) = 100*(1/2)^t would decrease for increasing values of t as b lies between 0 and 1. f(t) = 100*2^t would increase for increasing values of t, this is a exponential growth function.

For any exponential function f(x) = a*b^x, if b is less than 1 and greater than 0 it is a decay function and if b is greater than 1 it is a growth function.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial