# Exponential Growth

Another application of exponential function is Exponential Growth. If half-life applies to radioactive elements, this topic is usually about bacteria. Think of one bacterium, after a certain period of time it doubles itself, after another period of time the two bacteria double themselves. Now there are already 4 of them. After another period of time there are 8 of them and so on. But the normal thing is, there is not just one bacterium. There is usually a colony of them. Using exponential functions we can mathematically determine the number of bacteria in the colony after a certain period of time.

Formula:

Given an initial number of bacteria in a colony and multiply itself times after time . The number of bacteria (A_n) in the colony after time is given by the following formula:

**Sample Problem 1:**

A fictional bacterium called *Chenis madakis* doubles itself every 15 minutes; a colony of sample containing 100 healthy bacteria is under observation, how many bacteria are there at the end of one hour?

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Using the formula above,

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**Sample Problem 2:**

A certain type of bacteria multiplies itself 3 times every 4 hours. Find the size of the sample of the colony after 1 day if initially there are 1000 bacteria.

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**Sample Problem 3:**

*Celia kakaskakas *doubles itself every 5 minutes. How long will it take for it to make itself 4 times as many as its original number?

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eqn.1

Substitute from equation 1:

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### Dan

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