5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

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1. Evaluate 42 - |x - 7| if x = -3

2. Find 4.1 (-0.5)

Simplify each expression

3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9)

5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green?

6. Which of the following is a true statementStandardized Test Practice:

A CB D8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8

Lesson 10-6

Growth and Decay

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Objectives

• Solve problems involving exponential growth

• Solve problems involving exponential decay

Vocabulary

• Exponential growth –• • Exponential decay –

• Compound interest –

Key Concept

• xxxx

Example 1a

Population In 2000, the United States had a population of about 280 million, and a growth rate of about 0.85% per year. Write an equation to represent the population of the United States since the year 2000.

General equation for exponential growth

andor 0.0085

Simplify.

Answer: where y represents the population and t represents the number of years since 2000

Example 1b

According to the equation, what will be the population of the United States in the year 2010?

Equation for the population of the U.S.

or 10

Answer: In 2010, the population will be about 304,731,295.

Example 2Compound Interest When Jing May was born, her grandparents invested $1000 in a fixed rate savings account at a rate of 7% compounded annually. The money will go to Jing May when she turns 18 to help with her college expenses. What amount of money will Jing May receive from the investment?

Compound interest equation

Compound interest equation

Simplify.

Answer: She will receive about $3380.

Example 3aCharity During an economic recession, a charitable organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000.Write an equation to represent the charity’s donations since the beginning of the recession.

General equation for exponential decay

Answer: Simplify.

Example 3b

Charity During an economic recession, a charitable organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000.Estimate the amount of the donations 5 years after the start of the recession.

Answer: The amount of donations should be about $369,017.

Equation for the amount of donations

Example 4Depreciation Jackson and Elizabeth bought a house when they first married ten years ago. Since that time the value of the real estate in their neighborhood has declined 3% per year. If they initially paid $179,000 for their house, what is its value today?

General equation for exponential decay

Simplify.

Use a calculator.

Answer: Their house will be worth about $131,999.

Summary & Homework• Summary:

– Exponential Growth: y = C(1 + r)t, where y represents the final amount, C represents the initial amount, r represents the rate of growth expressed as a decimal and t represents time.

– Exponential Decay: y = C(1 – r)t, where y represents the final amount, C represents the initial amount, r represents the rate of decay expressed as a decimal and t represents time.

– Compound Interest: A = P(1 + r/n)nt, where A represents the amount of the investment, P represents the amount of the principal, n represents the number of times interest is compounded each year, r represents the rate of change of interest expressed as a decimal and t represents the number of years of the investment.

• Homework: – pg