Meet students taking the same courses as you are!Join a Numerade study group on Discord

Like

Report

Numerade Educator

Like

Report

Problem 1 Easy Difficulty

Explain why the values of an increasing exponential function will eventually overtake the values of an increasing linear function.

Answer

The values of an increasing exponential function will eventually overtake the value of an increasing function, because, linear functions have a constant rate of change whereas an exponential functions increase based on a percent of the original.

Discussion

You must be signed in to discuss.

Video Transcript

So we're going to compare linear functions to exponential functions and the differences in more rate of change. The rate of change of a linear function is a Constance. No matter how high you're current value, I will increase by the same amount per unit time anyway, like sir, um, whereas an exponential function is proportional with your current growth so roughly like, sir, as you can see, even if initially, the race of change of the exponential function is lower because the value is small, it will eventually win outs because proportional increase will always win out over a constant increase is almost both functions always increasing like so.