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### Course: College Algebra>Unit 13

Lesson 5: Interpreting the rate of change of exponential models

# Interpreting change in exponential models

Sal finds the factor by which a quantity changes over a single time unit in various exponential models.

## Want to join the conversation?

• Why 1.75 is as the same as 75% instead of 0.75?
• 75% does = 0.75
The problem is dealing with exponential growth in the number of branches.
So tree has its original number of branches (100% or 1) + growth of 75% (0.75)
1 (original) + 0.75 (growth) = new percentage = 1.75%
For example: 200 branches * 100% + 75% growth = 200(1) + 200 (0.75) = 200 (1.75) = 350

If the problem just used 0.75, then the number of branches would actually be shrinking by 25%
For example: 200 * 0.75 = 150 branches
This is fewer branches than we started with. So, the tree is not growing, its shrinking.

Hope this helps.
• I don't understand why the bear population would shrink by a factor of 2/3 rather than 1/3. When it asked, "what factor is the bear population shrinking by" isn't it asking for the factor in function of the population lost rather than the one remained?
• The question is asking for the factor. In this case the factor is (2/3). The population is decreasing by 1/3, but to get the third, you would multiply by two thirds.

example: 1 * 2/3 = 2/3
The 1 has decreased by one third to a solution of 2/3
• Sal says the bear population shrinks by a factor of 2/3, but this statement is just a double negative, if something shrinks by a factor <1, then it increases. So would it shrink by the reciprocal of 2/3? (So 3/2), or would it shrink by the difference of 1 and the original factor added to 1. Which would be (1 - 2/3 + 1 or 4/3).
• No, shrinking by a factor of 2/3 means the original amount is MULTIPLIED by 2/3, which means you have 2/3 of the original left.
• In the practice "Interpret change in exponential models" when given a question about finding percentage, if we are handed sat (0.75), why would this not be 75% for an answer. I've tried looking at the explanation but it doesn't make sense.
• How do you do the (0.81)^t ones, he doesn't explain that
• If you've got something like f(x) = 43*(0.81)^t, then it's like the second last example with 2/3 as a factor. If you have a factor that is smaller than 1, then the number still decreases.
• In the first exercise, something is increasing, so we get "...increases by a factor 1.5" or so. In the second exercise something decreases. Decreasing is the opposit of increasing, so we'd expect "...decreases nu a factor 1.5". Instead we get a decrease by a factor less than 1. Isn't a decrease by a factor less than one an increase? Just like an increase by a factor less than one is a decrease?
• Yes... to decrease a value using multiplication, you need to multiply by a value less than 1. Any value over 1 would increase the number.
• Why is Math so darn hard all the time?

:(
• Does the population of bears shrink by a factor or 2/3 or 1/3? It seems if there are 2/3 as many bears the next year, the population shrank by 1/3.
(1 vote)
• It did shrink by 1/3, but not by a factor of 1/3. A 'factor' is a term of multiplication. Since there are 2/3 as many bears, the population was multiplied by 2/3, so we say it shrunk by a factor of 2/3.
• So if n is 1 or more it grows and if it is less than one it shrinks?
(1 vote)
• Basically, if you have a function f that is exponential and can be expressed as:
`f(x) = a * b^x`, b determines the factor.

`If b < 1, then f(x) will decrease as x increases.If b > 1, then f(x) will increase as x increases.If b = 1, then no matter what x is, 1^x = 1, so it stays flat.`
• How can exponential growth and decay help us solve problems in the real world? How does this math subject affect and impact us throughout our lives? What is an example of exponential growth or decay in the real world?
• As we see in the video, exponential growth and decay can help us measure anything from the amount of a drug left in the body to the amount of radiation in an area.
(1 vote)