Warm Up April 111. Graph y = 4x. State the y-intercept. Then use the

graph to determine the approximate value of 40.6.

Determine whether the data in each table is a geometric sequence (exponential function). Explain why or why not.

2. 3.

4. A tournament begins with 64 teams. After each round, only half of the teams remain. Write an exponential function for the number of teams remaining after x rounds of play. How many teams remain after 3 rounds?

X 1 2 3 4

Y 0.5 1.5 2.5 3.5

X 2 4 6 8

Y 4 16 64 256

Exponential Growth

April 11th, 2013

Identifying an Exponential Function Examples:Does this table or rule represent an

exponential function?

Identifying an Exponential Function You Try:Does this table or rule represent an

exponential function?

Identify Determine whether the set of data displays

exponential behavior. Explain. X 0 1 2 3 4

Y 5 10 15 20 25

Evaluating an Exponential Function 1. Example: Suppose 30 flour beetles are

left undisturbed in a warehouse bin. The beetle population doubles each week. The function gives the population after weeks. How many beetles will there be after 56 days? 

Step 1: Convert 56 days to weeks.

Step 2: Evaluate for x = 8.

Example:

BUSINESS The amount of money spent at West Outlet Mall in Midtown continues to increase. The total T(x) in millions of dollars can be estimated by the function T(x)=12(1.12)x, where x is the number of years after it opened in 1995.

a) According to the function, find the amount of sales in 2006, 2008 and 2010.

b) Name the y-intercept.

c) What does it represent in this problem?

You Try 3. An initial population of 20 rabbits triples

every half year. The function gives the population after x half-year periods. How many rabbits will there be after 3 years?

Exponential GrowthExponential growth is an initial amount

that increases at a steady rate over time.

Exponential growth can be modeled by the function, where a > 0 and b > 1. The base b is the growth factor, which equals 1 plus the percent rate of change expressed as a decimal.

Exponential Growth y = a (b) x

Equation: A = P(1 + r)t. A represents the final amount. P represents the initial amount. r represents the rate of change expressed as a

decimal t represents time.

Key words to look for that tell you to use the formula is increase, appreciate and growth.

Examples

1. POPULATION The population of Johnson City in 1995 was 25,000. Since then, the population has grown at an average rate of 3.2% each year.

a. Write an equation to represent the population of Johnson City since 1995.

b. According to the equation, what will the population of Johnson City be in the year 2005?

2. Find the current value of a $125,000 home that was purchased, in 2010, if it appreciates at a 4% rate annually. Write the exponential function to model the situation, and find the amount after the specified time.

Examples

P =r =n = t =

What would n be for the following?

tn

n

rPA )1(

3. The Lieberman’s have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years.

4. Determine the amount of an investment if $300 is invested, at an interest rate of 6.75%, compounded semiannually for 20 years.

HomeworkWorkbook pg. 219 #1-8, 15,

16

Warm-Up April 12th Worksheet

Exponential Decay

April 19th, 2013

Identify Determine whether the set of data displays

exponential behavior. Explain To enter data:

STAT 1 ENTER L1 is x L2 is y

2nd Y= to turn stat plot on

ZOOM 9 to see graph.

X 0 2 4 6 8 10Y 64 32 16 8 4 2

Exponential DecayExponential Decay occurs when an

initial amount decreases at a steady rate over time.

Exponential decay can be modeled by the function --------- ,where a > 0 and b < 1. The base b is the decay factor, which equals 1 minus the percent rate of change expressed as a decimal.

Exponential Decayy = a (b) x

Equation: A = P(1 – r)t.A represents the final amount.P represents the initial amount.r represents the rate of decay

expressed as a decimal.t represents time.Key words to look for that tell you to

use the formula is decrease, depreciate and decay.

Examples1. The original price of a tractor was $45,000. The

value of the tractor decreases at a steady rate of 12% per year.

a. Write an equation to represent the value of the tractor since it was purchased.

b. What is the value of the tractor in 5 years?

Examples2. The kilopascal is a unit of measure for atmospheric

pressure. The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases about 11.5%. What is the approximate pressure at an altitude of 3000 m?

You Try 3. Find a value of a $20,000 car in five

years if it depreciates at a rate of 12% annually. Write the exponential function to model the situation, and find the amount after the specified time.

You Try4. A population of 1,860,000 decreases

1.5% per year for 12 years. Write the exponential function to model the situation, and find the amount after the specified time.

Practice Sheet Work with a partner (that means one

other person). This worksheet must be completed by the

end of class to earn participation. Turn in when complete.

If you and your partner are not on task I will separate you and you will work alone. So please stay on task!

Homework

Workbook pg. 219-220 #9-14, 18,

#20-23