<p>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</p><p>Create two charts determining how much money you will earn over the 30 days.</p><p>Day # $ Option A 1 $1000 2 $2000 3 $3000</p><p>Day # $ Option B 1 $0.01 2 $0.02 3 $0.04 Graph the points from each chart. Use different colors to represent each option. Choose an appropriate interval for x values and y values so you can fit your points on the graph. Part 2: Find equations representing each situation. 1. Enter your data into the graphing calculator (turn STAT PLOT on)</p><p>STAT </p><p>EDIT </p><p> enter “days” in L1</p><p> enter “$ - Option A” in L2</p><p>2. Compute a linear regression equation for the data. Round to 3 decimal places.</p><p>STAT</p><p>CALC</p><p>LinReg (Linear Regression)</p><p>Enter</p><p> y = </p><p>3. Enter the equation into Y1 = </p><p>4. Change your window size to make sense for the data.</p><p>Record your window here: Xmin = ______Xmax = ______</p><p>Ymin = ______Ymax = ______</p><p>5. Use the table in your calculator to answer the following:</p><p> a. Assume the payout continues past one month. After 65 days, how much money will you have if you choose Option A?</p><p> 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.</p><p>Write the equation here: y = ______</p><p>7. Enter the equation into Y2 = </p><p>8. Change your window size to make sense for the data.</p><p>Record your window here: Xmin = ______Xmax = ______</p><p>Ymin = ______Ymax = ______</p><p>9. Use the table in your calculator to answer the following:</p><p> a. Assume the payout continues past one month. After 35 days, how much money will you have if you choose Option B?</p><p> b. About how long will it take you to reach $44,000,000? 10. Which option (A or B) would you take?</p><p>11. Refer back to the exponential regression equation you wrote: ______</p><p>The first number should be your INITIAL amount of money.</p><p>The base is your “multiplier” or your “growth rate” since you doubled every day.</p><p>The exponent represents time.</p><p>When a quantity is growing exponentially at a given RATE, we use this model: f(x) = a∙bx a is </p><p> b is </p><p> x is </p><p>Set up an equation and solve each exponential word problem.</p><p>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?</p><p>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?</p><p>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? </p><p>For Homework, watch the following video and TAKE NOTES:</p><p>Exponential Growth – Word Problems https://www.youtube.com/watch?v=xcf8lt7VOv4</p>