Interpret an exponential graph in a real context

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Interpret an exponential graph in a real context

A repeated percentage change can give an exponential model. Starting with 80 units and increasing by 25% each step gives y = 80 × 1.25ⁿ. The multiplier stays fixed, but the absolute amount added grows because it is a percentage of the new total.

A graph can estimate when the model reaches a threshold. Whether fractional inputs are meaningful depends on the process: a continuous model can use fractional time, while a rule applied only after whole monthly updates may require a whole-number step.

An exponential model is an assumption about the process, not a promise of unlimited real growth. Population, financial and cooling contexts need their own limitations and units. State the range over which the model is intended to apply.

Worked example: A model doubles every hour from 12. Find the amount after three hours.

Use y = 12 × 2ⁿ.

Substitute n = 3.

Answer: 96 units.

Check your understanding: Does doubling mean adding 12 every hour?

Answer: No.

Why: The new amount is multiplied by two, so successive increases change.