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## Algebra (all content)

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

Lesson 18: Interpreting the rate of change of exponential models (Algebra 2 level)

# 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.
• 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.
• 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
• 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.
• Why is Math so darn hard all the time?

:(
• 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.
(1 vote)
• 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?
(1 vote)
• 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.
• 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.`