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# Difference Between Linear Function and Exponential Function

February 7, 2024
written by Sidra Batool

The main difference between linear and exponential functions is their rate of change. Linear functions have a constant rate, while exponential functions have a rate that continuously increases or decreases.

## Comparative Analysis of Linear Function and Exponential Function

### 1: Rate of Change

Linear:Â In linear functions, the rate of change isÂ constant. This means that for every equal increase in the input (x), the output (y) increases by the same amount. Imagine climbing a staircase – each step takes you the same distance higher.

Exponential:Â In exponential functions, the rate of changeÂ continuously increases or decreases. This means that for every equal increase in the input, the output increases (or decreases) by aÂ larger multiplier. Picture bacteria multiplying or radioactive decay – the change gets faster or slower over time.

### 2: Visually

Linear function:Â Graph is a straight line with a constant slope.

Exponential function:Â Graph is a curve that either bends upwards or downwards, getting steeper or shallower as it progresses.

### Examples

Linear:Â Distance traveled at a constant speed, cost of groceries with a fixed price per item.

Exponential:Â Population growth with constant birth rate, radioactive decay, and compound interest.

## Linear Function vs Exponential Function

Here is a table summary showing Difference Between Linear Function and Exponential Function:

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