# Exponential Growth and Decay

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Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths to help students learn how to solve exponential growth and decay word problems.

The following diagram shows the exponential growth and decay formula. Scroll down the page for more examples and solutions that use the exponential growth and decay formula.

Exponential Growth Function - Population
This video explains how to determine an exponential growth function from given information. Then it explains how to determine when a certain population will be reached and when it will double. Exponential Growth Function - Bacterial Growth
This video explains how to determine an exponential growth function from given information. Then it explains how to determine when a certain population will be reached..

Exponential Decay : C4 Edexcel January 2013 Q8
A bottle of water is put into a refrigerator. The temperature inside the refrigerator remains constant at 3 °C and t minutes after the bottle is placed in the refrigerator the temperature of the water in the bottle is θ°C.
The rate of change of the temperature of the water in the bottle is modelled by the differential equation,
dθ/dt = (3-θ)/125
(a) By solving the differential equation, show that,
θ = e–0.008t + 3
where A is a constant.

Given that the temperature of the water in the bottle when it was put in the refrigerator was 16°C,
(b) find the time taken for the temperature of the water in the bottle to fall to 10°C, giving your answer to the nearest minute Exponential Growth / Population Growth Problem
In this video, we know that a population is growing exponentially; we also know there were 200 bacteria 3 days ago and 1000 bacteria yesterday. How many bacteria will be present tomorrow? Compound Interest & Exponential Growth

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