Algebra II HG Section 7 1 Exploring Exponential

Algebra II H/G Section 7 -1 Exploring Exponential models

1) MAKING BALLOTS Sarah is helping the Student Government Association by making ballots for tonight’s election. She starts by cutting a sheet of paper in half. She then stacks the two pieces and cuts them in half. She stacks the resulting four pieces and cuts them in half. Sarah repeats this process, creating smaller and smaller pieces of paper. After each cut, Sarah counts the ballots and records the results in a table.

NUMBER OF CUTS NUMBER OF BALLOTS AREA (in 2) 0 1 324 1 2 3 4 5 6

2) Graph the information in the chart. What is the domain and range of each function? What is the yintercept of each function? Asymptote

Summary

Determine whether the functions represent exponential growth or decay without graphing and also find the y-intercept. exponential growth y-intercept: (0, 0. 25) exponential decay y-intercept: (0, 3)

5 a) Parker invested his $2000 in birthday money in an account that pays 5% annual interest compounded yearly. How much money will be there in the account after five years? $2552. 56

Exponential Growth model Number of time periods Growth rate written as a decimal Current Amount Growth factor

5 b) Will invested $2000 in an account. Will thinks he is smarter than Parker and invests his money into an account that pays 5% annual interest compounded quarterly. How much money will be there in the account after five years? $2564. 07

5 c) Josh invested $2000 in an account. Josh thinks he is smarter than both Parker and Will and invests his money into an account that pays 5% annual interest compounded monthly. How much money will be there in the account after five years? about $2567. 23

COMPOUND INTEREST FORMULA

Exponential Decay model Number of time periods Current Amount Rate of decay written as a decimal quantity Decay factor

6) The population of certain animal species decreases at a rate of 4% per year. If the population of this species was 200 in 2006. How many of these species will be there in 2018? about 122

Challenge: Determine which situation matches the graph a) A population of 95 tigers decreases 5% yearly. b) A population of 85 tigers increases 33. 8% yearly. c) A population of 85 tigers decreases 22% yearly. d) A population of 95 tigers decreases 78. 85% yearly. e) A population of 95 tigers increases 38. 45% yearly. ANSWER : d