Instructions
Fill out the questions in the pictures below.
Copy of Grayson Dotson - [Template] ExpGrowthDecaySE * @ Saving- 6 Share G File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago no $ A 7 150% . Normal text * A - 11 + B I U A / C P O . = = 3 13 B E EE X Q. ME Editing A 31 Activity A: Get the Gizmo ready: Student Exploration: Exponen. Exponential Select the CONTROLS tab. growth . Unselect all checkboxes. 1. In the Gizmo, set C to 5.00 and r to 0.20 to graph the function y = 5(1 + 0.2)'. Then select the TABLE tab. + A. "Graph the function B. on the grid below. Then fill in the missing y-values in the table. Hand draw on the grid or click on it to select EDIT to use the drawing tool. (You can adjust the MIN and MAX values in the Gizmo table if you like.) y = 5(1 + 0.2)' 12 t y 10 0 5 1 6 6 2 7.2 3 8.64 2 4 10.37 -2 2 4 B. What is the initial value of the function (y-value when t = 0)? C. Each time t increases by 1, what happens to the y-values? (By what percent do they increase?) Explain. D. What part of the formula represents the initial value? E. What part of the formula represents percent of growth? +Copy of Grayson Dotson - [Template] ExpGrowthDecaySE # @ 6 Share G File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago no $ A 7 200% . Normal text Arial - 11 + B I U A / CO P O . B B 3 B B B . BE X Editing A 4. Nina deposits $400 in an account that earns 4% interest, compounded annually. onen... A. What is the initial value of the account? The initial value of the account is $400. B. What function represents the balance after t years? y=400(1.04)^t represents balance in t years C. What is the value of the account after 5 years? (Use a calculator.) The value of the account after 5 years becomes $486.66116096. D. Graph your function in the Gizmo. (Hint: Enter C = 4 in the Gizmo and let y = the balance of the account in hundreds.) Check your answer using the TABLE tab. E. Select Show probe. Drag the probe slowly to the right. When will Nina will have more than Nina have more than $600? (Click and drag the graph, or click - to $600 in 11 years. zoom out.) F. About how long will it take for the balance to double? Nina needs at least 18 years for her balance to be doubled. +Copy of Grayson Dotson - [Template] ExpGrowthDecaySE * @ 6 Share File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago In A 7 200% Normal text Arial - 11 + B I U A / GO P . . = = = BE E . EV E EX Editing A 31 + 3. In 2000, the population of Dullville was about 95,000. Over the next decade, the population decreased by 18%. For the questions below, assume this rate of decay will continue. A. What function models the population after t decades? B. Graph your function. (Hint: Let y = population in thousands. To enter the initial value, type 95 in the field next to the C slider and hit Enter.) Then select Show probe and drag it to the right. About what will the population be after 30 years (t = 3 decades)? C. Roughly when will the population be half the initial population? +Copy of Grayson Dotson - [3rd Block] Google Doc Version of ArithGeoSequenceSE * S 6 Share G File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago 150% Normal text Arial - 11.5 + B J U A / G P O - E . BE E . E . E E X A 31 4. Set a, to 3, r to 1, and n to 10. Vary the r slider for values greater than 1. let... A. Describe the graph from left to right. B. Vary the r slider for values between 0 and 1. How does the graph change? Why? + C. Describe the graph when r is negative. Why is this? 5. Explain why a sequence like 12, 12, 12, 12, ... is both arithmetic and geometric. 6. Write the explicit formula for the geometric sequence shown in the graph to the right. Then check your answer in the Gizmo. an n 2 6 8 10 12 14 -2 -4 -6 -8 +Copy of Grayson Dotson - [3rd Block] Google Doc Version of ArithGeoSequenceSE * S 6 Share G File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago n a $ A 7 150% Normal text Arial - 11.5 + B J U A . GO P O . = 13 B E . E E X A 31 4. Write an explicit formula for each sequence described below. Then check your answers in the Gizmo. (Recall that "d" means "common difference" and "," means "common ratio.") net... A. An arithmetic sequence with d 0. a = + C. A sequence with all positive terms, approaching zero. a = 4 7 11:30Copy of Grayson Dotson - [3rd Block] Google Doc Version of ArithGeoSequenceSE * S 6 Share G File Edit View Insert Format Tools Add-ons Help Last edit was seconds ago 125% Normal text Arial - 11.5 + B J U A . G P O . = 13 B E. E E X A 31 2. An arithmetic sequence has a first term of 2 and a common difference of 0.5. (Do not graph this sequence dent Exploration: Arithmet in the Gizmo yet.) mo Warm-up A. What are the first six terms of this sequence? B. If you were to graph these terms, what would the + coordinates of the six points be? Check this in the Gizmo. C. The points of this graph lie on a line. What is the slope of the line? Explain why that makes sense. 3. On the previous page, you looked at an arithmetic sequence with a first term of 2, and a common difference of 0.5. A. What is the explicit formula for this arithmetic sequence? B. In the space to the right, simplify the formula you wrote above. C. How does the simplified formula above relate to the graph of this sequence? An arithmetic conlianea honine with the tarme 5 7 +
