Exponential+Functions-Target+D-Modeling+Data-Guided+Learning

Exponential Functions Target D: Write an exponential function to model a contextual situation

 * [[image:Discuss this.png width="208" height="117"]] || After watching the video Heidi thinks that the population growth of the world is linear and Rachel thinks that the population growth is exponential. Whom do you agree with and why?

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There are many real life situations that can be modeled using a linear relationship. Within the context of these situations there needs to be a constant rate of change. But what if there isn’t? (To determine if a linear relationship or exponential relationship exists refer to Exponential Functions Target C). In some instances, the rate of change is not constant, but increases or decreases by a growth factor. When this occurs, we use an exponential growth/decay model to represent the situation.

Here is the exponential growth/decay model: math y=a(1\pm r)^{t}\ math The symbol ± is used to refer to both addition and subtraction. If a situation represented exponential growth, use addition. If the situation represents exponential decay, use subtraction. So what do all of those variables represent? The “//a//” represents the initial amount, the “//r//” represents the rate at which something is growing (increasing) or decaying (decreasing), “//t//” represents the time that has or will pass and the "y" represents the ending amount or value at time "t". There are certain key terms that can help you differentiate between exponential growth and exponential decay. For growth, you may see terms such as increases, earns, accumulates, and so on. For decay some key terms may be decrease, depreciates, loses, etc.

Here are just a few examples of when you would use the exponential growth/decay model:
 * finding the balance of a savings account after a given period of time
 * determining the value of a car after so many years
 * estimating/calculating a city’s population

__**Example 1:**__ A college graduate accepts a job at an advertising agency. The job has a salary of $40,000 per year, plus a pay increase of 2% per year. How much will the graduate be making in 10 years? media type="custom" key="28203453"

__**Example 2:**__ Francine just bought a new car for $32,000. She plans on keeping the car as long as she is still able to get $18,000 when she finally decides to sell it. If the average depreciation rate for cars is 15% per year, how many years will she own the car before she needs to sell it? media type="custom" key="28203461"


 * Exponential Functions-Target D-Modeling Data-Quick Check**

1) You deposit $125 into a savings account that earns 5% annual interest, compounded yearly. Your friend deposits $200 into a savings account that earns 3.75% interest compounded yearly. Who will have a higher balance in their account when they reach 17 years old if no other deposits are made?

Exponential Functions-Target D-Modeling Data-Quick Check Solutions