Exponential Function 1/29/2013

Warm – Up 2 1/25/2013

HW 5.3 Check a) xxxxxyy b) 4*4*4xxx2*2*2*2*2*2yyyyyy c)(x+3)(x+3) e)5*5*5*5*5*5yyyyyyzzzzzz f) (3x-1)(3x-1)(3x-1) 2. a) x^3q^4 b) 3^3w^3x^2y 3. c^77 b)m^22n^29 c)15x^12y^15 4a) arith, d=6 b) geom, r=-2 c) arith, d=11 d) geom, r=1/2 5. -20, -27, -34, -41, -48, -55, -62

HW 5.4 Check A, d=-4 2. G, r=4 3. A, d= 4 4. G, r=10 5. 2, 6, 18, 54, 162 6. -1, 1, 3, 5, 7 7. 0, 4, 8, 12, 16 8. 10, 5, 2.5, 1.25, 0.625 9. 16, 48, 80, 112, 144, 176 Total distance= 576

The geometric sequence from the Brown Tree Snake problem (1, 5, 25, 125, 625 . . .) can be written in the form of a table, as shown below: 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). See below:

The graph of the table is NOT a straight line. The graph is NOT linear in nature Because the sequence is NOT arithmetic.

The graph is curved 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.

The Ladybug Invasion As a biology project, Tamara is studying the growth of a ladybug population. She starts her experiment with 5 ladybugs. The next month she counts 15 ladybugs. 1) The ladybug population is growing arithmetically. How many beetles can Tamara expect to find after 2, 3, and 4 months? Write the sequence. 2) What is the common difference? 3) Now put the sequence into a table in the space below.

One Grain of Rice The book One Grain of Rice by Demi, is about a village in India that does not have enough food to support its population because of famine and because the raja kept all of the rice for himself. The main character Rani cleverly tricks the raja into giving rice to the village. Read the following excerpt from the book to fill in the table below.

India Long ago in India, there lived a raja who believed that he was wise and fair. But every year he kept nearly all of the people’s rice for himself. Then when famine came, the raja refused to share the rice, and the people went hungry. Then a village girl named Rani devises a clever plan. She does a good deed for the raja, and in return, the raja lets her choose her reward. Rani asks for just one grain of rice, doubled every day for thirty days. Through the surprising power of doubling, Rani teaches the raja a lesson about what it truly means to be wise and fair.

HW. 5.5 Don’t forget Quiz on Friday!