Graphing Exponential Functions Date: ______

Algebra 2 Name: ______Graphing Exponential Functions Date: ______Would you rather: A. Receive $1000 a day for a month (30 days) B. Double your money each day for a month (30 days), starting with $0.01

Create two charts determining how much money you will earn over the 30 days.

Day # $ Option A 1 $1000 2 $2000 3 $3000

Day # $ Option B 1 $0.01 2 $0.02 3 $0.04 Graph the points from each chart. Use different colors to represent each option. Choose an appropriate interval for x values and y values so you can fit your points on the graph. Part 2: Find equations representing each situation. 1. Enter your data into the graphing calculator (turn STAT PLOT on)

enter “days” in L1

enter “$ - Option A” in L2

2. Compute a linear regression equation for the data. Round to 3 decimal places.

LinReg (Linear Regression)

3. Enter the equation into Y1 =

4. Change your window size to make sense for the data.

Record your window here: Xmin = ______Xmax = ______

Ymin = ______Ymax = ______

5. Use the table in your calculator to answer the following:

a. Assume the payout continues past one month. After 65 days, how much money will you have if you choose Option A?

b. About how long will it take you to reach $250,000? 6. Complete steps #1 – 2 for Option B. Except for Step 2, use ExpReg (Exponential Regression) instead of LinReg.

Write the equation here: y = ______

7. Enter the equation into Y2 =

8. Change your window size to make sense for the data.

Record your window here: Xmin = ______Xmax = ______

Ymin = ______Ymax = ______

9. Use the table in your calculator to answer the following:

a. Assume the payout continues past one month. After 35 days, how much money will you have if you choose Option B?

b. About how long will it take you to reach $44,000,000? 10. Which option (A or B) would you take?

11. Refer back to the exponential regression equation you wrote: ______

The first number should be your INITIAL amount of money.

The base is your “multiplier” or your “growth rate” since you doubled every day.

The exponent represents time.

When a quantity is growing exponentially at a given RATE, we use this model: f(x) = a∙bx a is

Set up an equation and solve each exponential word problem.

1. The value of a painting is $12,000 in 1990 and doubles its value each year. What is the painting’s value in 1996?

2. The turtle population in Huntingdon Valley triples every 6 months. If there were 20 turtles in January 2016, how many turtles were there in January of 2018? 3. The number of bacteria present in a given petri dish doubles every hour. If the experiment begins with 25 bacteria, how many bacteria are present after 12 hours?

Part 2: What if your growth rate is not doubling or tripling? What if your growth rate is 10% per day? Or 8% per year?

For Homework, watch the following video and TAKE NOTES:

Exponential Growth – Word Problems https://www.youtube.com/watch?v=xcf8lt7VOv4