7.1 - Exponential Growth and Decay

7.1 - Exponential Growth and Decay

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Objective

To model exponential growth and decay

Essential Understanding

Exponential Function

A function with a variable as an exponent

Exponential Function

Exponential Behavior

​There are two types of exponential behavior:

Exponential Growth: as the value of x increases, the value of y increases. if a>0 and b>0, the function represents exponential growth

Exponential Decay: as the value of x increases, the value of y decreases, approaching 0. If a>0 and 0<b<1, the function represents exponential decay.

In either case, the y-intercept is (0, a), the domain is all real numbers, the asymptote is y=0, and the range is y>0.

(An asymptote is a line that a graph approaches as x or y increases in absolute value.

Exponential Growth Function

Exponential Decay Function

Open Ended

Does the function $$f\left(x\right)=1.5^x$$  model growth or decay? How do you know?

Let's try another

Multiple Choice

A new vehicle loses a certain percentage of its value every year. Which graph could represent the value of the vehicle over time?

Multiple Choice

A couple buys a house for $200,000. The value of the house appreciates at 7% per year. Which equation models this situation?

• $$y=200,000\cdot0.93^x$$  

• $$y=200,000\cdot1.07^x$$  

• $$y=200,000\cdot7^x$$  

• $$y=200,000\cdot x^7$$  

Open Ended

A couple buys a house for $200,000. The value of the house appreciates at 7% per year. How much has the value of the house increased after 4 years?

Poll

We can do this, right?

• Yes

• Maybe, leaning yes

• Maybe, leaning no

• No