Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential...

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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? Backup 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/exponentialgrowth/exponentialmodelsinrealworld.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 wildlife 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

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