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## Algebra (all content)

### Course: Algebra (all content)>Unit 11

Lesson 17: Introduction to rate of exponential growth and decay

# Exponential growth & decay word problems

How do you solve word problems involving exponential growth and decay? In this video, you will learn how to use a table and a formula to find the percentage of a radioactive substance that remains after a certain time. You will also see how a common ratio, which is the factor by which the quantity changes every time period, determines the rate of change. You will use a calculator to apply the formula and get the answers. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• Is there a way to do this without using a calculator?
• Yes, long, long, LONG multiplication, for example 1.08 to the 8th power can easily be solved without a calculator by 1.08*1.08*1.08*1.08*1.08*1.08*1.08*1.08, but using a calculator makes things WAY faster and simpler.
• i don't understand how he gets 1.08 when it is 1(200)?
• ok um this was asked a while ago, but I'm not clear about the question.
1.08 is the 100 percent plus 8 percent of the increase per year, and the 1(200) is the starting number of restaurants... I'm in eighth grade though, but I think thats what it means
• Would it be reasonable to say that exponential functions are a mathematical explanation of various observations of the natural world?
• Yes. Exponential functions tracks continuous growth over the course of time. The common real world examples are bacteria growth, compound interest and radioactive decay.
• So for exponential growth, when finding the rate you add 1? Than in decay you subtract one? because i am partially confused on if i'm just adding for both or subtracting for both.
• YES, because in class instead of making a chart we use the formula v=c(1+r)^t t=time r=rate iof increase and v=c(1-r)^t where r now equals rate of decrease...so yeas rate if increase = +1 rate of decrease = -1......
Hope i helped your confusion =]
• @ Why did Sal add 1?
(1 vote)
• @ he explains why
• how do you do this in exponential equation form with out the table
• You can do an exponential equation without a table and going straight to the equation, Y=C(1+/- r)^T with C being the starting value, the + being for a growth problem, the - being for a decay problem, the r being the percent increase or decrease, and the T being the time. Sal just uses a table to help him explain why the equation makes sense.
• So, if the standard form of an exponential growth or decay function is y=C(1+r)^t, would C be the initial amount and r would be the percentage at which the amount would increase or decrease?
• how did u come up with 100 on the first one..?
• Because it has not started decaying as time has not started.
• at , I don't understand why you use 1.08, and at , why did you use 0.965 and not 0.035?
• at
The substance decays by 3.5%. This means you take away 3.5% from the original.
The original = 100%
100% - 3.5% = 96.5% or 0.965

at
The number of stores increases 8% each year. This means you are adding 8% to the original.
The original = 100%
100% + 8% = 108% or 1.08

Hope this helps.