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Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential Growth Functions 8.5
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### Transcript of Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential...

• Objectives: Today we will

Write and solve exponential growth functions.Graph exponential growth functions.Vocabulary: exponential growthExponential Growth Functions8.5

• Would You Rather ?!?!After arguing with your family that you should get a higher allowance your family offers you two allowance options. Either, they will give you \$20 each week or they will give you one penny on the first day and double your allowance every day for 31 days. What option would you pick? Back-up your answer with math!

• The Solution

1 \$.012 \$.023 \$.044 \$.085 \$.166 \$.327 \$.648 \$1.289 \$2.5610 \$5.1211 \$10.2412 \$20.4813 \$40.9614 \$81.9215 \$163.8416 \$327.6817 \$655.3618 \$1310.7219 \$2621.4420 \$5242.8821 \$10,485.7622 \$20,971.5223 \$41,943.0424 \$83,886.0825 \$167,772.1626 \$335,544.3227 \$671,088.6428 \$1,342,177.2829 \$2,684,354.5630 \$5,368,709.1231 \$10,737,418.24

• Real World Exponential Growth Examplehttp://www.mathwarehouse.com/exponential-growth/exponential-models-in-real-world.php

• Exponential Growth Functions8.5A quantity is growing exponentially if it increases by the same percent in each time period.C is the initial amount.t is the time period.(1 + r) is the growth factor, r is the growth rate.Exponential growth always has a growth rate greater than or equal to one. (1 + r) 1y = C (1 + r)tSometimes use P instead of CNote: measure of rate and time MUST be in the same time unit

• Example 1Compound InterestYou deposit \$1500 in an account that pays 2.3% interest compounded yearly,What was the initial principal (C) invested?What is the growth rate (r)? The growth factor?Using the equation y = C(1+r)t, write the equation that models this situation. Then figure out how much money would you have after 2 years if you didnt deposit any more money?C or P = \$1500Growth rate (r) is 0.023. The growth factor is 1.023.y = \$1569.79

• Example 2Compound InterestA savings certificate of \$1000 pay 6.5% annual interest compounded yearly. First, write the equation that models this situation. Then figure out what is the balance when the certificate matures after 5 years? \$1370.09

• What is the percent increase each year?Write a model for the number of rabbits in any given year.Find the number of rabbits after 5 years.Example 3Exponential Growth ModelA population of 20 rabbits is released into a wild-life region. The population triples each year for 5 years.200% 4860 rabbitsy =20(1+2.00)t

• Exponential Growth ModelGraph the growth of the rabbits.Make a table of values, plot the points in a coordinate plane, and draw a smooth curve through the points.P = 20 ( 3 ) tHere, the large growth factor of 3 corresponds to a rapid increaseExample 4

• Write a model for the weight during the first 6 week.Find the weight at the end of six weeks.Example 5Exponential Growth ModelA newly hatched channel catfish typically weighs about .3 grams. During the first 6 weeks of life, its growth is approximately exponential, increasing by about 10% a day.y =.3(1+.10)t 16.4 grams

• Example 6Exponential Growth ModelGraph Make a table of values, plot the points in a coordinate plane, and draw a smooth curve through the points.y =3(1.10)t

• Write a model for the number of bacteria at any hour.Find the number of bacteria after 8 hours.Example 7Exponential Growth ModelAn experiment started with 100 bacteria. They double in number every hour.y =100(1+1.00)t 25,600 bacteria

• pgs. 480-481 #1, 4, 5, 14, 15, 21, 22, 24Homework