Alg1 Notes 9.3M.notebook May 01, Warm Up

Size: px

Start display at page:

Download "Alg1 Notes 9.3M.notebook May 01, Warm Up"

Donald Atkins
6 years ago
Views:

9.3 Warm Up Tell whether each set of ordered pairs satisfies an exponential function. Explain your answer. 1. {(0, 0), (1, 2), (2, 16), (3, 54)} 2. {(0, 5), (1, 2.

009) x models residential energy consumption in quadrillion Btu where x is the number of years after 2003. What will residential energy consumption be in 2013? 5.

02) x gives the population, in millions, x years after 2000. Using this model, in about what year will the population reach 30 million? Simplify each expression. 6.

1 9.3 Warm Up Tell whether each set of ordered pairs satisfies an exponential function. Explain your answer. 1. {(0, 0), (1, 2), (2, 16), (3, 54)} 2. {(0, 5), (1, 2.5), (2, 1.25), (3, 0.625)} 3. Graph y = 0.5(3) x. 4. The function y = 11.6(1.009) x models residential energy consumption in quadrillion Btu where x is the number of years after What will residential energy consumption be in 2013? 5. In 2000, the population of Texas was about 21 million, and it was growing by about 2% per year. At this growth rate, the function f(x) = 21(1.02) x gives the population, in millions, x years after Using this model, in about what year will the population reach 30 million? Simplify each expression. 6. ( ) ( ) The first term of a geometric sequence is 3 and the common ratio is 2. What is the 5th term of the sequence? 10. The function f(x) = 2(4) x models an insect population after x days. What is the population after 3 days? Chapter 9 Warm up 3 answers 4. 5.

2 9 3 Exponential Growth and Decay Give a Hand to the Welcher!!!! Get out a calculator and see if you can evaluate: 9.3 Exponential Growth and Decay Learning Targets: 1. Solve exponential growth and decay problems. How we use this... Exponential growth and decay describe many real world situations, such as the value of artwork.

3 I. Exponential Growth Exponential growth occurs when an quantity increases by the same rate r in each period t. When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. I. Exponential Growth The original value of a painting is $9,000 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. y = a(1 + r) t

y = a(1 + r) t I. Exponential Growth A common application of exponential growth is compound interest.

4 You Try! A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an exponential growth function to model this situation. Then find the sculpture s value in y = a(1 + r) t I. Exponential Growth A common application of exponential growth is compound interest. Recall that simple interest is earned or paid only on the principal. Compound interest is interest earned or paid on both the principal and previously earned interest.

II. Finance Application Write a compound interest function to model each situation. Then find the balance after the given number of years. A. $1200 invested at a rate of 2% compounded quarterly; 3 years.

5 II. Finance Application Write a compound interest function to model each situation. Then find the balance after the given number of years. A. $1200 invested at a rate of 2% compounded quarterly; 3 years. B. $15,000 invested at a rate of 4.8% compounded monthly; 2 years. You Try! Write a compound interest function to model each situation. Then find the balance after the given number of years. A. $1200 invested at a rate of 3.5% compounded quarterly; 4 years B. $4000 invested at a rate of 3% compounded monthly; 8 years

Exponential Decay A) The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people.

6 III. Exponential Decay Exponential decay occurs when a quantity decreases by the same rate r in each time period t. Just like exponential growth, the value of the quantity at any given time can be calculated by using the rate and the original amount. Growth vs. Decay III. Exponential Decay A) The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people. Write an exponential decay function to model this situation. Then find the population in B) The fish population in a local stream is decreasing at a rate of 3% per year. The original population was 48,000. Write an exponential decay function to model this situation. Then find the population after 7 years.

Science Application Astatine 218 has a half life of 2 seconds.

7 III. Exponential Decay A common application of exponential decay is half life. The half life of a substance is the time it takes for one half of the substance to decay into another substance. IV. Science Application Astatine 218 has a half life of 2 seconds. Find the amount left from a 500 gram sample of astatine 218 after 10 seconds. Step 1 Find t, the number of half lives in the given time period. Step 2 A = P(0.5) t = 500(0.5) 5 = There are grams of Astatine 218 remaining after 10 seconds.

8 IV. Science Application Astatine 218 has a half life of 2 seconds. Find the amount left from a 500 gram sample of astatine 218 after 1 minute. Step 1 Find t, the number of half lives in the given time period. Step 2 A = P(0.5) t There are grams of Astatine 218 remaining after 1 minute. You Try! A) Cesium 137 has a half life of 30 years. Find the amount of cesium 137 left from a 100 milligram sample after 180 years. Step 1 Find t, the number of half lives in the given time period. Step 2 A = P(0.5) t Bismuth 210 has a half life of 5 days. B) Find the amount of bismuth 210 left from a 100 gram sample after 5 weeks. (Hint: Change 5 weeks to days.) Step 1 Find t, the number of half lives in the given time period. Step 2 A = P(0.5) t

9 Assignment 9.3 Page 639, 1 9, odd, 37 41, odd, 45 48

9.6 Notes Part I Exponential Growth and Decay

9.6 Notes Part I Exponential Growth and Decay I. Exponential Growth y C(1 r) t Time Final Amount Initial Amount Rate of Change Ex 1: The original value of a painting is $9000 and the value increases by