WARM UP Write down objective and homework in agenda. Lay out homework (WB 8-6 #1-26) Homework (Charity Donations worksheet)

Warm Up Determine if the sequence is geometric. If it is, find the common ratio. -1, 6, -36, 216, . . . -1, 1, 4, 8, . . .  4, 16, 36, 64, . . . -3, -15, -75, -375, . . -2, -4, -8, -16, . . . 1, -5, 25, -125, . . .

Warm Up Determine if the sequence is geometric. If it is, find the common ratio. -1, 6, -36, 216, . . . Yes, r = -6 -1, 1, 4, 8, . . . NO  4, 16, 36, 64, . . . NO -3, -15, -75, -375, . . Yes r = 5 -2, -4, -8, -16, . . Yes r = 2 1, -5, 25, -125, . . Yes, r =-5

The Brown Tree Snake was first introduced to Guam in year 0 The Brown Tree Snake was first introduced to Guam in year 0. At the end of year 1, five snakes were found; at the end of year 2, twenty-five snakes were discovered, and so on. Since we now have a table of the information, a graph can be drawn, where the year is the independent variable (x) and the number of snakes is the dependent variable (y).

Notice that the graph of the table is not a straight line, which we already know because it was a geometric sequence Rather, the graph is curved and moves in a growing fashion very rapidly due to the fact that the common ratio r of this sequence is 5. The curved graph of this problem situation is known as an exponential growth function.

An exponential growth function occurs when the common ratio r is greater than one. Tables and graphs make viewing the data from the problem situation easier to see and we can easily see from either the table or graph that in year 3, the snake population is 125.

Let us look at a similar population growth for a certain kind of lizard in both a table and graph. Use either one or both to answer the questions below.

What information does the point (2, 40) on the graph tell you? Notice from the shape of the graph that the information is exponential in nature. What information does the point (2, 40) on the graph tell you?  At year two there were 40 lizards What information does the point (1, 20) on the graph tell you? At year one there were 20 lizards When will the population exceed 100 lizards? At year 4

Explain how to find the common ratio, using either the table or graph. Look at the y values to find the pattern If the information from the table were written as a sequence, what is the initial term? 10 How could we find the 10th term in the table, graph, or sequence? Keep using the sequence, 10,240

The Mice Problem You Try! A population of mice has a growth factor (otherwise known as the common ratio) of 3. After 1 month, there are 36 mice. After 2 months, there are 108 mice. How many mice were in the population initially (at 0 months)? Explain how you found this number. Write a sequence to show how the mice population is growing. Is this sequence arithmetic or geometric? Explain how you know. Now, put your sequence into the table below. Is the graph of the table going to be a straight line or a curve? Explain your answer

The Mice Problem You Try! A population of mice has a growth factor (otherwise known as the common ratio) of 3. After 1 month, there are 36 mice. After 2 months, there are 108 mice. How many mice were in the population initially (at 0 months)? Explain how you found this number. 12 mice; used the common ratio of 3 Write a sequence to show how the mice population is growing. 12, 36, 108, 324 Is this sequence arithmetic or geometric? Explain how you know. Geometric; the population triples every month Now, put your sequence into the table below. Is the graph of the table going to be a straight line or a curve? Explain your answer Curved because it’s a geometric sequence/exponential

Who Wants to be Rich?! Students at a local school want to have a quiz show called Who Wants to Be Rich? Contestants will be asked a series of questions. A contestant will play until he or she misses a question. The total prize money will grow with each question answered correctly. Lucy and Pedro are on the prize winnings committee and have different views of how prize winning should be awarded. Their plans are outlined below for your consideration. Review them by answering the questions following the plans. Remember that the committee has a fixed amount of money to use for this quiz show.

Who wants to be rich? Lucy proposes that a contestant receives $5 for answering the first question correctly. For each additional correct answer, the total prize would increase by $10. For Lucy’s proposal, complete the table below. Sketch the graph of correctly answered questions 1-10. Be sure to title your graph and label the axes. How much money would a contestant win if he or she correctly answered 6 questions? How much money would a contestant win if he or she correctly answered 9 questions? Number of questions 1 2 3 4 5 6 7 8 9 10 Total prize

Who wants to be rich? Number of questions 1 2 3 4 5 6 7 8 9 10 Total prize   How many questions would a contestant need to answer correctly to win at least $50? How many questions would a contestant need to answer correctly to win at least $75? How is this table growing? Is this a linear or exponential growth pattern?

For Pedro’s proposal, complete the table below. Pedro also proposes that the first question should be worth $5. However, he thinks a contestant’s winnings should double with each subsequent answer. For Pedro’s proposal, complete the table below.   Sketch the graph of correctly answered questions 1-10. How much money would a contestant win if he or she correctly answered 6 questions? How much money would a contestant win if he or she correctly answered 9 questions? Number of questions 1 2 3 4 5 6 7 8 9 10 Total prize

Number of questions 1 2 3 4 5 6 7 8 9 10 Total prize   How many questions would a contestant need to answer correctly to win at least $50? How many questions would a contestant need to answer correctly to win at least $75? How is this table growing? Is this a linear or exponential growth pattern?

Which is better?! Which plan is better for the contestants? Explain your reasoning. Which plan is better for the school? Explain your reasoning.