1. Warm Up

2. Exponential Regressions and Test Review

3. Exponential Models for data… In a research experiment, a population of fruit flies was introduced into an environment and recorded below. Elapsed time (in days) Population of fruit flies 025 228 633 1039 1549 1959 2474 3096 1)Use your calculator to write an exponential model to best fit the data and PASTE it into Y= 2)Use your model to predict the number of fruit flies after 40 days. 3)Use your model to determine the elapsed time when then population of fruit flies was 65.

4. Time (L1) Temp (L2) 1184.3 5164.0 7155.1 10143.7 14130.5 18119.9 20115.2 23109.26 28101 Time (L1) Temp (L2) 3295.728 3889.56 4584.36 5081.62 6077.83 7075.53 8074.14 8873.43 10072.78 A temperature probe was placed in a cup of hot coffee then removed and held in a room that was 70°. The temperature of the probe was recorded below.

5. TRASHKETBALL

6. Test Review 1)Determine a function for the logistic function whose graph is shown in the figure. 2) What is the total value after 6 years of an initial investment of $2250 that earns 7% APR compounded quarterly?

7. CALCULATOR ACTIVE The population of a town is 350,000 and is increasing at the rate of 4.65% every year. 1.Write a function that determines the population of the town in terms of the number of years. 2.After how many years will the population be one million? (Round to 3 decimal places) 3.What will be the population in 30 years?

8. 1.The half life of a certain substance is 60 days. How much of 24 grams will be left after 100 days? 2.How long will it take an account that compounds continuously at 6% APR to double in value? 3.A certain account has accumulated $10,000 in 5 years. The account has earned 4%APR compounded monthly. What was the initial deposit? CALCULATOR ACTIVE

9. Calculator Active The table shows the population of Aurora, CO for selected years between 1950 and 2003. 1.Use logistic regression to find a logistic curve to model the data. Write your model rounding to 3 decimal places. 2.Based on the regression equation, what is the carrying capacity of Aurora, CO.? (3 decimal places) 3.Based on the regression equation, after how many years will the population exceed 300,000? (3 decimal places) 4.Based on the regression equation, what was the (approximate) population in 1965? (nearest whole number). Years after 1950 Population 011,421 2074,974 30158,588 40222,103 50275,923 53290,418

10. NO Calculator Solve for x: 1.log 4 256 = x 2. 3.

11. NO Calculator

12. 1) log b 1 = x 3) Simplify completely

13. NO Calculator Solve for x: 1.log 2 x 2 – log 2 (x+3) = 2 2.log 4 x + log 4 (x – 3) = log 7 7

14. 1.Write as a single logarithm: 2.Write as simplified logarithms

15. Solve for x. NO CALCULATOR 1) 2 + 3e -x = 82) 3e 2x + 8e x = 3

16. Solve for x. NO CALCULATOR 1) 8 x+1 = 102)

17. Calculator Active The winning times in the women’s 100 meter freestyle event at the Summer Olympic Games since 1952 are shown. Let x = 0 be 1900… 1)Assuming the data approaches a horizontal asymptote of y = 52, write an exponential model that best fits the data. 2)According to this model, what would be the winning time for the women’s freestyle at the 2008 Olympics? Round to 3 decimal places. Years Since 1900 5256606872768084889296100 Time 66.86261.26058.655.754.855.954.954.654.553.8