Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build an exponential function from two data points
Problem
Build \(f(x)=a\cdot~b^x\) through \((0,5)\) and \((1,15)\). Use the input-zero equation to find \(a\), use the second point to solve \(b\), and verify both ordered pairs in the final model.
Big Picture
What this problem is really about
An input-zero point isolates the exponential coefficient because the base contributes a factor of one. We’ll use that point first, substitute the second point to solve the base as an output ratio rather than a difference, and verify both ordered pairs in the completed model.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
