Lesson 2 Exponential Growth & Decay Notes. 2)Factor completely: 3) Solve, 3x 2-5x = 3, round your answer to the nearest thousandth.

Transcription

1 1) 2)Factor completely: 18x 2-21x ) Solve, 3x 2-5x = 3, round your answer to the nearest thousandth.

2 Exponential Functions: GROWTH & DECAY *Many real world phenomena can be modeled by functions that describe how things grow or decay as time passes. Examples of such phenomena include the studies of populations, bacteria, the AIDS virus, radioactive substances, electricity, temperatures and credit payments, to mention a few.*

3 The exponential functions for growth and decay are represented as follows: Exponential Growth Exponential Decay

4 You deposit $1500 in an account that pays 6% interest compounded yearly. Find the balance after 5 years. Balance after 5 years: You deposit $3500 in an account that pays 8.4% interest compounded yearly. Find the balance after 9 years. Balance after 9 years:

5 3. Value this years: Value in 2020? 4. day? Value this years: Value in 2020?

6

7 Classwork: 1.) A population of Protozoa grows at a constant relative rate of.475 per day. On day zero, the population consists of two members. Find the population size after 10 days. 2.) The City of Schenectady currently has a population of approximately 66 thousand people. If the city lost approximately 2.8% of its population every year, in seven years, what would the new population be? 3.) Mendelevium-259 has a half-life of 6 hours. If you currently have 50 kg of Mendelevium-259, in a day how many kg of Mendelevium-259 would you still possess?

8

9 One of the most common examples of exponential growth deals with bacteria. Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. For example, if we start with only one bacteria which can double every hour, by the end of one day we will have over 16 million bacteria.

10 There is a well-known fable about a man from India who invented the game of chess, as a gift for his king. The king was so pleased with the game that he offered to grant the man any request within reason. The man asked for one grain of wheat to be placed on the first square of the chess board, two grains to be placed on the second square, four on the third, eight on the fourth, etc., doubling the number of grains of wheat each time, until all 64 squares on the board had been used. The king, thinking this to be a small request, agreed. A chess board has 64 squares. How many grains of wheat did the king have to place on the 64 square of the chess board?

11 Lesson #2: Homework 1.) In 1995, there were 85 rabbits in Central Park. The population increased by 12% each year. How many rabbits were in Central Park in 2005? 2.) A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1000 bacteria and the bacteria are doubling every half hour. How many bacteria will there be after 2 and a half hours? 3.) At the start of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with rate 0.02, what will be the population after 5 hours? 4.) Richard buys a car for $34,500 in 2005 and it depreciates on average at a rate of11% every year. What would be the estimated value of Richard s car in 2012? 5.) A cup of coffee contains about 100 mg of caffeine. Every hour 16% of the amount of caffeine is metabolized and eliminated. a. Write an equation for, the amount of caffeine in the body as a function of, the number of hours since the coffee was consumed. b. How much caffeine is in the body after five hours, to the nearest hundredth of a milligram? After a day? 6.) The population of a particular species of bird increases at 2.5% annually. If there are 246 birds living in a region, how many will be there after 10 years? 7.) From 1983 to 1997, the ratio of students per computer at a school has dropped by about 16.8% per year. If there were 103 students per computer in 1983, what was the number of students per computer in 1997? 8.) The rural town of San Filipposville has been losing population at a rate of 5.8% per year for the last 10 years. It has a current population of 12,500. What will the population be in 8 years if it keeps declining at the same rate? 9.) Andy Graham has a savings certificate that is currently worth $10, and pays 6.5% interest compounded yearly. What is the balance when the certificate matures in 5 years? 10.) Scientists, Matos and Massarelli, were working on an experiment which started with 10 bacteria. The bacteria doubled every hour for 24 hours. Write an exponential model for this situation and use it to find the number of bacteria after 480 minutes.