1. © 2010 Pearson Education, Inc. All rights reserved Uninhibited Exponential Growth Uninhibited Exponential Decay 4.6 – Modeling with Exponential and Logarithmic Functions

2. © 2010 Pearson Education, Inc. All rights reserved Example The population of the United States was approximately 227 million in 1980 and 282 million in 2000. Estimate the population in the year 2010. Find k2010 4.6 – Modeling with Exponential and Logarithmic Functions

3. © 2010 Pearson Education, Inc. All rights reserved Example A radioactive material has a half-life of 700 years. If there were ten grams initially, how much would remain after 300 years? When will the material weigh 7.5 grams? Find k300 years7.5 grams 4.6 – Modeling with Exponential and Logarithmic Functions

4. © 2010 Pearson Education, Inc. All rights reserved Example Jack’s grandfather started an account for him on the day he was born. The account will have $25,000 in it on Jack’s 25 th birthday. If the interest rate is 6.2%, how much was the initial investment made by Jack’s grandfather? 4.6 – Modeling with Exponential and Logarithmic Functions

5. © 2010 Pearson Education, Inc. All rights reserved Example Find A(10)Find r Rebecca invested $15,000 into an account. In 20 years, it grows to $110,835.84? What was the interest rate of the account? What was the value of the account after 10 years? 4.6 – Modeling with Exponential and Logarithmic Functions

6. A bone was found in a dig-site and had lost 91.4% of its carbon-14. The half-life of carbon-14 is 5370 years. How old is the bone? Find carbon-14 in bone Find k 8.6% of carbon-14 4.6 – Modeling with Exponential and Logarithmic Functions

7. The logistic equation is another model for population growth. Limited Growth This is used when there are factors preventing the population from exceeding some limiting value L, such as a limitation on food, living space, or other natural resources. The logistic equation: 4.6 – Modeling with Exponential and Logarithmic Functions

8. Limited Growth Example: How many people are initially infected? 4.6 – Modeling with Exponential and Logarithmic Functions

9. Limited Growth Example: How many people are infected after 5 days and 12 days? 4.6 – Modeling with Exponential and Logarithmic Functions

10. Limited Growth Example: How many days will it take the disease to infect 2000 people? 4.6 – Modeling with Exponential and Logarithmic Functions

11. Limited Growth Example: Determine the limiting value of N(t) 4.6 – Modeling with Exponential and Logarithmic Functions t grows without bounds

12. 4.6 – Modeling with Exponential and Logarithmic Functions