Warm Up for Quiz No Calculator!

1. Warm Up for Quiz No Calculator! • If log671 = 2.379, what is 62.379? • Evaluate: • Evaluate: • Evaluate: • Expand: • Condense: 3[log x + log(x-2)] – ¼ log w

2. Quiz Time! • When finished, make sure your name is on it, turn it in face down on the cart and pick up notes for today.

3. Example 1: The population of Eagle City was 10,000 people in 1900. It has been increasing at a steady rate of 2.5% per year.

4. Example 1: The population of Eagle City was 10,000 people in 1900. It has been increasing at a steady rate of 2.5% per year. • Let n = the number of years since 1900 and A(n) = the population of Eagle city. • What type of function is A(n)? Explain how you know. • Write a function A(n) that defines the population in terms of the years since 1900.

5. Example 1: The population of Eagle City was 10,000 people in 1900. It has been increasing at a steady rate of 2.5% per year. • Use your function from #1 to predict the population of Eagle City at the end of 1937. • Use your equation to predict when the population will be 100,000 people.

6. Example 2: The population of Trojanville in the year 2000 was 235,000 and continues to decrease at the rate of 1.5% every year.

7. Example 2: The population of Trojanville in the year 2000 was 235,000 and continues to decrease at the rate of 1.5% every year. • Write a function A(n) that defines the population in terms of the years since 2000. • Use your function from #1 to predict the population of Trojanville after 5 years. • Use your equation to predict when the population will be 200,000 people.

8. General Population Equation P(n) = P(0)(1 ± r )n

9. Example 3: The population of Smallville was 678 in 1955 and 1,410 in 1970. Assuming exponential growth, what would be the growth rate per year?

10. Example 4: Suppose a culture of 100 bacteria are put in a petri dish and the culture doubles every hour. • Let n = the # of hours and A(n) = the amount of bacteria in the dish. Write a function A(n) that defines the amount of bacteria in terms of the number of hours. • Use your function to predict the amount of bacteria after 1 day. • Use your function to predict when there will be 350,000 bacteria

11. Example 5: Suppose the half-life of a certain radioactive substance is 20 days and that there are 5 grams present initially. • Write a function for the amount of substance that is present after t days. • Use your function to predict when there will only be 1 gram left. • Use your function to predict the amount of substance present after 30 days.

12. General Half-Life Equation P(n) = P(0)(½)n/half-life

13. Your Turn

14. Example 6: You deposit $5000 in a trust fund at an annual interest rate of 7.5%, compounded monthly. • How much interest are you earning every month? • Write a function for the amount of money that is present after n years. • How much time will it take for your money to double?

15. General $Money$ Equation Compound Interest P(n) = P(0)(1 + r/n)nt Compound Continuously P(n)= P(0)ert

16. Your Turn Determine when an investment of $1500 accumulates to a value of $2280 if the investment earns interest at a rate of 7%APR compounded monthly. You deposit $1000 in a savings account that earns 4% interest compounded continuously How much money will you have in 10 years? How long will it take for you to accumulate $3200