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Warm-Up 7

Warm-Up 7. Identify each variable as the dependent variable or the independent for each of the following pairs of items the circumference of a circle the measure of the radius the price of a single compact disc the total price of three compact discs

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Warm-Up 7

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  1. Warm-Up 7 Identify each variable as the dependent variable or the independent for each of the following pairs of items • the circumference of a circle the measure of the radius • the price of a single compact disc the total price of three compact discs • time spent studying for a test score on the test • number of hours it takes to type a paper the length of the paper • amount of your monthly loan payment the number of years you need to pay back the loan • number of tickets sold for a benefit play the amount of money made

  2. HW 5.9 Check

  3. Practice with Compound Interest • Find the balance of a checking account that has $54,000 compounded quarterly at 12% for 9 years.

  4. Find the balance of a checking account that has $900 compounded semiannually at 5% for 15 years.

  5. You deposit $1600 in a bank account. Find the balance after 3 years for each of the following situations: • a. The account pays 2.5% annual interest compounded monthly. • b. The account pays 1.75% annual interest compounded quarterly. • c. The account pays 4% annual interest compounded yearly.

  6. Lets look at the sheet from yesterday…. • What did we notice when you add or subtract a number from the EXPONENT? How does the graph shift? • What did we notice when we add or subtract from the WHOLE thing (not in the exponent)? How does the graph shift?

  7. Translations y = 2x  h k h determines the shift LEFT/RIGHT +h Left -h right k determines a shift UP/DOWN +k up -k down

  8. Describe the transformations

  9. Write the new equation given the transformations

  10. Part of an Exponential Graph Horizontal Asymptote: A horizontal line that the graph “flat lines” at Y-Intercept: Where the graph crosses the y-axis.

  11. Identify Horizontal Asymptotes and y-intercept

  12. Identify Horizontal Asymptotes and y-intercept

  13. Exponential Decay

  14. Drug Filtering Assume that your kidneys can filter out 25% of a drug in your blood every 4 hours. You take one 1000-milligram dose of the drug. Fill in the table showing the amount of the drug in your blood as a function of time. The first three data points are already completed. Round each value to the nearest milligram

  15. How many milligrams of the drug are in your blood after 2 days? • Will you ever completely remove the drug from your system? Explain your reasoning. • A blood test is able to detect the presence of the drug if there is at least 0.1 mg in your blood. How many days will it take before the test will come back negative? Explain your answer.

  16. Recall: y = a•bx/n Initial (starting) value = a Growth or Decay Factor = b x is the variable, so we change that value based on what we are looking for! Where n is our period. Remember that the growth or decay factor is related to how the quantities are changing. Growth: Doubling = 2, Tripling = 3. Decay: Losing half = Losing a third =

  17. Exponential Decay When b is between 0 and 1! Growth : b is greater than 1

  18. If the rate of increase or decrease is a percent : we use a base of 1 + r for growth or 1 – r for decay THIS WILL BE YOUR B!

  19. Ex 1. Suppose the depreciation of a car is 15% each year? • Write a function to model the cost of a $25,000 car x years from now. • How much is the car worth in 5 years?

  20. Ex 2: Your parents increase your allowance by 20% each year. Suppose your current allowance is $40. • Write a function to model the cost of your allowance x years from now. • How much is your allowance the worth in 3 years?

  21. Complete the 2 practice problems

  22. Other Drug Filtering Problems 1. Assume that your kidneys can filter out 10% of a drug in your blood every 6 hours. You take one 200-milligram dose of the drug. Fill in the table showing the amount of the drug in your blood as a function of time. The first two data points are already completed. Round each value to the nearest milligram.

  23. How many milligrams of the drug are in your blood after 2 days? • A blood test is able to detect the presence of the drug if there is at least 0.1 mg in your blood. How many days will it take before the test will come back negative? Explain your answer.

  24. 2. Calculate the amount of drug remaining in the blood in the original lesson, but instead of taking just one dose of the drug, now take a new dose of 1000 mg every four hours. Assume the kidneys can still filter out 25% of the drug in your blood every four hours. Have students make a complete a table and graph of this situation.

  25. How do the results differ from the situation explored during the main lesson? Refer to the data table and graph to justify your response. • How many milligrams of the drug are in your blood after 2 days?

  26. Coming up… Homework tonight – 5.10 QUIZ Friday 2/8 Unit 5 TEST – Wednesday 2/13

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