# Exponential relationship growth and decay

### Exponential growth vs. decay (practice) | Khan Academy

Exponential word problems almost always work off the growth / decay formula, A = Pert, For instance, all of the following represent the same relationship. We may use the exponential growth function in applications involving Exponential growth and decay graphs have a distinctive shape, as we can see in the. Learn how to construct, analyze, graph, and interpret basic exponential functions of Exponential function graph Exponential growth & decay word problems.

We have learned that taking the log is an easy way to isolate an exponent.

### Exponential growth & decay word problems (video) | Khan Academy

Here, we can plug in any y value and obtain our x value. We must be careful, because we cannot take the log of any value less than or equal to 0.

Let's try a harder example We would go about this as we would we any other equation, treating the term with the exponent as a variable until we have to deal with it. This is a bit of a mess, but it does the trick!

• Exponential growth & decay word problems
• Exponential growth & decay
• Exponential Functions

We have successfully isolated x and can find any coordinate of the equation. In general Compound Interest In finance, exponential functions are prevelent in dealing with calculating interest. The compound interest formula is a very important exponential equation. Compound Interest Formula Where A is the ending amount, P is the beginning value, or principle value, r is the interest rate usually a fractionn is the number of compoundings a year, and t is the total number of years.

### Exponential growth & decay | Algebra I | Math | Khan Academy

We will see that this formula simplifies to the exponential functions we are accustomed to. Regarding n, if interest is compounded once a year, it would be considered annually and n would be 1.

If twice a year, it would be considered semi-annually and n would be 2 similarly, quarterly would be 4, monthly would be 12, and so on. Since the interest rate is expressed in years, the time must be expressed in years as well.

What is the ending amount after 10 years? This is the form of an exponential function with base 1. Suppose you want to know how many years until you have dollars, how many years will it take? It would take about 3 years. By varying the frequency in which the interest is compounded or the rate, the interest can be changed dramatically. Though this formula is important for managing money and calculating interest given a bank's interest rates and how many times it is compounded yearly, what if we compounded it continuously?

In other words, what if we took the time t to infinity? We discussed compounding interest at different increments per year, but what if we keep going? Similar to pi, the value of e is irrational. Approximated to two decimal places, it is equal to 2. No other function has this trait. This pattern of growth should make intuitive sense: As more reindeer populate the island, more births occur. And so the population increases more rapidly as time goes on, resulting in the curved, concave-up shape of the graph — untilat least.

Graph of assumed population growth of the reindeer herd on St.

Actual population measurements are indicated on the graph. The introduction, increase, and crash of reindeer on St. Journal of Wildlife Management, 32 2: Relationships with Two Variables for more information. The rapid increase in the number of reindeer on St. Matthew Island can be described with an exponential equation, and is called exponential growth.

This type of growth and its opposite, exponential decay is a common natural phenomenon, and thus exponential equations are frequently used in all branches of science.

And oftentimes you'll see it written this way. You have your initial amount times your common ratio, 0. This is how much you're going to have left after n hours.

## Exponential Growth and Decay

Well, now we can answer the question. After 6 hours how much are we going to have left?

Well, we're going to have times 0. And we could use a calculator to figure out what that is. Let's use our trusty calculator. So we have times 0. This is all in percentages. Let's do another one of these. So we have, Nadia owns a chain of fast food restaurants that operated stores in So let's think about the same thing.

So let's say years after And let's talk about how many stores Nadia is operating, her fast food chain. So itself is 0 years after And she is operating stores.

Then inwhich is 1 year afterhow many is she going to be operating? And you're going to see, the common ratio here is 1. Let me make that clear.