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Intro to Exponential Functions

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Intro to Exponential Functions

Lesson 3.1

View differences using spreadsheet

- Suppose you have a choice of two different jobs at graduation
- Start at $30,000 with a 6% per year increase
- Start at $40,000 with $1200 per year raise

- Which should you choose?
- One is linear growth
- One is exponential growth

- How do we get each nextvalue for Option A?
- When is Option A better?
- When is Option B better?
- Rate of increase a constant $1200
- Rate of increase changing
- Percent of increase is a constant
- Ratio of successive years is 1.06

- Consider a savings account with compounded yearly income
- You have $100 in the account
- You receive 5% annual interest

View completed table

- Completed table

- Table of results from calculator
- Set y= screen y1(x)=100*1.05^x
- Choose Table (Diamond Y)

- Graph of results

- Population growth often modeled by exponential function
- Half life of radioactive materials modeled by exponential function

- Recall formulanew balance = old balance + 0.05 * old balance
- Another way of writing the formulanew balance = 1.05 * old balance
- Why equivalent?
- Growth factor: 1 + interest rate as a fraction

- Consider a medication
- Patient takes 100 mg
- Once it is taken, body filters medication out over period of time
- Suppose it removes 15% of what is present in the blood stream every hour

Fill in the rest of the table

What is the growth factor?

- Completed chart
- Graph

Growth Factor = 0.85

Note: when growth factor < 1, exponential is a decreasing function

- For our medication example when does the amount of medication amount to less than 5 mg
- Graph the functionfor 0 < t < 25
- Use the graph todetermine when

- All exponential functions have the general format:
- Where
- A = initial value
- B = growth factor
- t = number of time periods

- When B > 1
- When B < 1

View results of B>1, B<1 with spreadsheet

- Lesson 3.1A
- Page 112
- Exercises1 – 23 odd
- Lesson 3.1B
- Pg 113
- Exercises25 – 37 odd