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### Course: Algebra 2>Unit 7

Lesson 3: Advanced interpretation of exponential models

# Exponential models: FAQ

## What is an exponential model?

An exponential model is a type of function that shows how a quantity grows exponentially over time. We often use exponential models to represent things like population growth, radioactive decay, and compound interest.

## Where are exponential models used in the real world?

Exponential models are used all over the place! As we mentioned earlier, they can be used to model population growth, radioactive decay, and compound interest. But they can also be used to model things like bacteria growth, the spread of an infectious disease, and even the growth of a social media account.

## What is a "rate of change"?

In mathematics, the rate of change tells us how quickly a quantity is changing over time. For an exponential model, the rate of change gives us information about how quickly the quantity grows (or decays) over time.

## What does "advanced interpretation" of an exponential model mean?

In this context, "advanced interpretation" refers to being able to take an exponential model and understand what the different parts of it mean. For example, we should be able to figure out what the initial value is, how quickly the quantity is growing, and what the trend will be over time.

## Want to join the conversation?

• If Bob invests \$900 into an account that gets 1.89% interest rate per month, what is the rate of change 8 years from now?
• - The initial amount is 900
- The rate of change is 1 + 0.0189 per month (+1.89%)
- 8 years is 8*12 months

You get:
900*1.0189^(8*12)
• how do I know when to convert my common ratio

for example in the first video of this lesson we see sal changed 1.06 to 1.0058 but when I moved on to the exercise after that video none of the problems needed me to convert the common ratio. Do I only convert it if it's a percentage?
• Are you referring to https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp-model/x2ec2f6f830c9fb89:interpret-exp/v/interpreting-change-in-exponential-models-changing-units, at ?
I think there's some confusion here...
The exponential function was `A(t) = 315*1.06^t` for `t` decades, but the video's question asked for yearly increase. Plugging in `A(0.1)` is `1` year since, and he divided this by the initial `A(0)`. This will give him the yearly increase, which is `1.06^(0.1)` or approximately `1.0058`. He did not change `1.06` to `1.0058`, rather he gave that as the answer to the problem that was asking for yearly increase.

I think you already know if they give "increase by 2%" you make the base `1 + 2%` or `1.02`, and if they give "decrease by 4.5%" you make the base `1 - 4.5%` or `0.955`. That's when you sort of convert the base.

Hope this clarified things!