Chapter 9.3 Exponential Growth and Decay.notebook
April 06, 2017
Homework Questions???
Bellwork:
1) Write the equation of the line in slope­intercept form.
a. Slope = 3, (­1, 4) is on the line
b. (2, ­3) and (4, 1) are on the line.
2) Graph the following equation, use x = ­1, 0, 1, 2, 3. Are the functions, increasing, decreasing or neither.
y = 4 (½)x
Apr 8­7:43 AM
Apr 8­10:19 AM
We use models of exponential growth and decay to describe real world situations such as, interest rates for loans, populations, half­life of chemicals.
Chapter 9.3 Exponential Growth and Decay
Solve Problems involving exponential growth.
Apr 8­10:20 AM
Exponential Growth
Exponential Decay y = final amount
a = original amount
r = rate(decimal)
t = time
Apr 8­10:20 AM
Exponential Growth: 1) Identify if the following situations would be exponential growth or decay?
a. The bird population in a wooded area is increasing by 4% each year from 1250.
2) The original value of a painting is $9000 and the value increases by 7% each year. Write an exponential growth function to model this situation. Then find the painting's value in 15 years. Identify the parts of the formula and substitute in the given values.
b. A small town's population was 9,000 in 2005 and is decreasing at a rate of 35 every year.
c. You invest $800 at an annual rate of 6%. Apr 8­10:29 AM
3) The bird population in a wooded area is increasing by 4% each year from 1250. Find the population after 7 years. Apr 8­10:33 AM
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Chapter 9.3 Exponential Growth and Decay.notebook
April 06, 2017
One of the most common applications of exponential growth is in compound interest.
4) Write a compound interest function to model each situation. Then find the balance after the given number of years.
Compound Interest: interest earned or paid on both the principal and previously earned interest. a. $1200 invested at a rate of 2% compounded quarterly for three years.
Compound Interest
A = balance after t years
P = Principal/original amount
r = annual interest rate (decimal)
n = # times compounded per year
t = time in years
b. $15,000 borrowed at a rate of 4.8% compounded monthly for 2 years. How many times would it be compounded in a year if it was compounded:
annually?
quarterly?
semi­annually?
monthly?
daily?
Apr 8­10:36 AM
Apr 8­10:40 AM
5) Write a compound interest function to model each situation. Then find the balance after the given number of years.
a. $500 invested at a rate of 5% compounded daily for 10 years.
Chapter 9.3(b) Exponential Growth and Decay
Solve Problems involving exponential decay.
b. $50 borrowed at a rate of 3% compounded semi­annually for 5 years. Mar 31­2:26 PM
Mar 31­2:26 PM
Exponential Decay: 6) The population of a town is decreasing at a rate of 3% per year. In 2000, there were 1700 people. Write an exponential function to model this situation. Then find the population in 2012.
Identify the parts of the formula and substitute in the given values.
Exponential Decay: 8) A car bought for $24,000 depreciates at a rate of 10% annual. What is the cars value after 5 years. 7) Monthly car sales for a certain type of car are $350,000 and are decreasing at a rate of 3% per month. What are the car sales for this car in 6 months?
Apr 8­10:42 AM
Mar 31­2:28 PM
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Chapter 9.3 Exponential Growth and Decay.notebook
Exponential Decay is used often to find the half­life of different substances.
Half­life: time it takes for one­half of the substance to decay into another substance.
April 06, 2017
9) Astatine­218 has a half­life of 2 seconds.
a. Find the amount left from a 500 gram sample of astatine­218 after 10 seconds.
Half­life
A = Final Amount
P = original amount
t = # of half­lives in a given period of time
Apr 8­10:47 AM
b. Find the amount of left from a 1,000 gram sample after 1 minute.
Apr 8­10:50 AM
10) Technetium­99 has a half­life of 6 hours.
a. Find the amount left from a 500 gram sample after 2 days.
Homework
P. 639­640 #1­35 (odds)
b. Find the amount of left from a 1,000 gram sample after 3 days.
Mar 31­2:29 PM
Apr 8­11:48 AM
Mar 31­12:32 PM
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