Nonlinear Relationship Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Determine whether \(y = 2^x\) is linear or nonlinear by examining the ratio \(y_{n+1}/y_n\) for \(x = 0, 1, 2, 3\).

Solution

  1. 1
    Values: \(y(0)=1, y(1)=2, y(2)=4, y(3)=8\).
  2. 2
    Ratios: \(2/1=2, 4/2=2, 8/4=2\) — constant multiplicative ratio.
  3. 3
    Differences: \(2-1=1, 4-2=2, 8-4=4\) — NOT constant.
  4. 4
    This is exponential (nonlinear), not linear.

Answer

Nonlinear (exponential) — constant ratio, not constant difference
Linear functions have constant additive differences. Exponential functions have constant multiplicative ratios. \(y=2^x\) doubles each step → exponential growth.

About Nonlinear Relationship

A relationship between two quantities where the rate of change is not constant—the graph is curved, not a straight line.

Learn more about Nonlinear Relationship →

More Nonlinear Relationship Examples

Example 1 medium

The area of a square is (A = x^2). Compare how (A) changes when (x) goes from 1 to 2, then 2 to 3. I

Example 2 hard

For (f(x) = x^2 - 4x + 3), find the vertex and determine whether the parabola opens up or down.

Example 3 medium

For (y = x^2), calculate values at (x = -2, -1, 0, 1, 2). Is the graph symmetric?

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