Honors Math 2 ~ Fall 2014 4
Unit 4: Radical and Exponential Functions
By the end of the unit students will be able to:
· Extend the properties of exponents to rational exponents.
· Use common logs to solve exponential equations.
· Interpret functions that arise in applications in terms of the context for exponential functions.
· Graph exponential functions by their key features.
· Write expressions in equivalent forms to solve problems with exponentials and common logarithms.
· Graph exponential functions, replace f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k
Day / Date / Lesson / Assignment1 / Thurs.
Oct. 9 / Monomial Rules/ Properties of Exponents / Homework 4-1
2 / Fri.
Oct. 10 / Re-write exponents as radicals / Homework 4-2
3 / Mon.
Oct. 13 / Solve Radical Equations / Homework 4-3
4 / Tues.
Oct. 14 / Exponential Growth and Decay / Homework 4-4
5 / Wed.
Oct. 15 / PSAT Day / Complete HW 4-4
Thurs.
Oct. 16 / Quiz Days 1-3
Exponential Form Given 2 points / Homework 4-5
6 / Fri.
Oct. 17 /
Introduction to Logarithms
/ Homework 4-67 / Mon.
Oct. 20 /
Solving using Logarithms
/ Homework 4-78 / Tues.
Oct. 21 /
Graphing Exponential and Logarithmic Equations
/ Homework 4-89 / Wed.
Oct. 22 /
Review for Unit 4 Test
/ Review SheetSTUDY!!
10 / Thurs.
Oct. 23 /
Unit 4 Test
Homework 4-1
Find the value of x in each of the following expressions in problems 1-6
Simplify the radicals in problems 7-12
1) 7x∙72=75 / 2) 2-3∙2-x=27 / 3) 632∙6x=364) 454x=1 / 5) 565x=1254 / 6) 4x13=16
7) /
8) /
9)
10) /
11) /
12)
Homework 4-2
Homework 4-3
1.) / 2.)3.) / 4.)
5.) / 6.)
7.) / 8.)
9.) / 10.)
11.) The velocity of a free-falling object is given by where h is the distance in feet the object has fallen and g is acceleration due to gravity in feet per second squared. The value of g depends on your altitude. If an object hits the ground with a velocity of 25 feet per second, from what height was it dropped in each of the following situations?
a.) You are standing on earth, so g = 32 ft/s2.
b.) You are on a space shuttle, so g = 29 ft/s2.
c.) You are on the moon, so g = 0.009ft/s2.
Common Core Math II Name Date
Homework 4-4 : Exponential Growth & Decay
1POPULATION
In 1990, Florida’s population was about 13 million. Since1990, the state’s population has grown about 1.7% each year. This means that Florida’s population is growing exponentially.
Year / Population1990
1991
1992
1993
1994
a) Write an explicit function in the form y=abx that models the values in the table.
b) What does x represent in your function?
c) What is the “a” value in the equation and what does it represent in this context?
d) What is the “b” value in the equation and what does it represent in this context?
2 HEALTHCARE
Since 1985, the daily cost of patient care in community hospitals in the United States has increased about 8.1% per year. In 1985, such hospital costs were an average of $460 per day.
a) Write an equation to model the cost of hospital care. Let x = the number of years after 1985.
b) Find the approximate cost per day in 2012.
c) When was the cost per day $1000
d) When was the cost per day $2000?
3HALF-LIFE
To treat some forms of cancer, doctors use Iodine-131 which has a half-life of 8 days. If a patient received 12 millicuries of Iodine-131, how much of the substance will remain in the patient 2 weeks later?
4 SAVINGS
Suppose your parents deposited $1500 in an account paying 6.5% interest compounded annually when you were born.
a) Find the account balance after 18 years.
b) What would be the difference in the balance after 18 years if the interest rate in the original problem was 8% instead of 6.5%?
c) What would be the difference in the balance if the interest was 6.5% and was compounded monthly instead of annually.
5 HEALTH
Since 1980, the number of gallons of whole milk each person in the US drinks in a year has decreased 4.1% each year. In1980, each person drank an average of 16.5 gallons of whole milk per year.
Year / Population1980
1981
1982
1983
1984
a) Write a recursive function for the data in the table.
b) Write an explicit function in the form y=abx that models the values in the table. Define your variables.
c) According to this same trend, how many gallons of milk did a person drink in a year in 1970?
6 WASHINGTON, D.C.
The model y=604000(0.982)x represents the population in Washington, D.C. x years after 1990.
a) How many people were there in 1990?
b) What percentage growth or decay does this model imply?
c) Write a recursive function to represent the same model as the provided explicit function.
d) Suppose the current trend continues, predict the number of people in DC now.
e) Suppose the current trend continues, when will the population of DC be approximately half what it was in 1990?
Homework 4-5
1) Using the points (2, 12.6) and (5, 42.525).
a) Find the exponential function that contains the points. Show you work.
b) Rewrite the function so that the exponent of the function is simply x.
2) When the brown tree snake is introduced to Guam during World War II by the US military it devastated the local ecosystem when its population grew exponentially. If 1 snake was accidentally brought to Guam in 1945 and it was estimated that there were 625 snakes in 1949, write an equation for the situation and use it to predict how many snakes there were in 1955. In your equation, let x=number of years after 1945. Show your work.
3) The water hyacinth that was introduced to North Carolina from Brazil ended up clogging our waterways and altering the chemistry of the water. We’re not certain exactly when the water hyacinth was introduced, but there were 76.9 square miles of water hyacinths in 1984. Ten years later, there were 80793.6 square miles of water hyacinth. Using this information, calculate when there was less than 0.1 square miles of this invasive plant in our waterways.
4) The intensity of light also decays exponentially with each additional colored get that is added over a spotlight. With three gels over the light, the intensity of light was 900 watts per square centimeter. After two more gels were added, the intensity dropped to 600 watts per square centimeter.
a) Write an equation for the situation. Show our work.
b) Use your equation to determine the intensity of the light with 7 colored gels over it.
Guided Practice with Logarithmic Functions
1) Graph the exponential function and its inverse on graph at right. Make a table if necessary.
Y = 2x
Y = log2 x
Graph the following transformations of the function y = log10 x on the coordinate planes. Determine the domain, range, and asymptotes of each transformation. Describe the transformations.
2) y = log10 x – 6 6) y = -log10 (x + 2) 7) y = log10 2x
Domain: Domain: Domain:
Range: Range: Range:
Asymptotes: Asymptotes: Asymptotes:
Description: Description: Description: