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Name: _____________________________ Period: _____________ Date: ______________ Chapter #7: Exponentials Functions Review Sheet Write the formula for Questions #1-7. 1. Arithmetic Sequence 2. Geometric Sequence 3. Common Difference 4. Common Ratio 5. Exponential Decay 6. Exponential Growth 7. Compound Interest Answer all of the following. Show all work for the following problems including all necessary formulas and substitutions. 8. Find the next term of the sequence 2, -10, 50, … 10. If 𝑓(𝑥) = 5(3)𝑥 , find the value of f (2). 12. The expression (22 )(25 ) is equivalent to (1) 27 (3) 47 (2) 210 (4) 410 9. Which expression is equivalent to (2x2)3? 11. The expression (10𝑤 2 ) 5𝑤 3 is equivalent to 13. Which expression is equivalent to x-2? (1) 1 𝑥2 (2) -2x (3) x2 (4) 1 𝑥 −2 2 14. If the first term of a geometric sequence is 3 and the common ratio is 3, find the 7th term. 16. The table below shows the average yearly balance in a savings computations account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited. 15. What is the value of 20 + 2-2? 17. A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth? Which type of function best models the given data? (1) linear function with a negative rate of change (2) linear function with a positive rate of change (3) exponential decay function (4) exponential growth function 18. The table below represents the function F. x y -1 2 0 3 1 4.5 2 6.75 3 10.125 The equation that represents this function is (1) F(x) = 3(1.5)x (2) F(x) = 1.5x (3) F(x) = (1.5)x + 3 (4) F(x) = 2x + 3.275 19. Which of the following graphs represent exponential decay? (1) (2) (3) (4) Answer all parts to each of the following. Partial credit is awarded. 21. The function f(t) = 100(1.05)t models the growth of a fruit fly population, where f(t) is the number of flies and t is time in days. In the function f (t), explain what 1.05 and 100 represent. 20. Kristen invests $5,000 in a bank. The bank pays 6% interest compounded monthly. Write an equation that can be used to find A, her account balance after t years. Show all work for the following. Partial credit is awarded. Be sure to show all formulas and substitutions necessary for full credit. 22. A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period. Time in Minutes Temperature in oF 0 2 4 6 8 10 180.2 165.8 146.3 135.4 127.7 110.5 a. Write an exponential regression equation for the data, rounding all values to the nearest hundredth. b. Using your equation from part a, predict the temperature of the soup after 15 minutes. Round to the nearest tenth. 23. Solve the system graphically: y = 5(3)x y = -2x + 5 24. In 2000, 2200 students attended Polaris High School. The enrollment has been declining 2% annually. a. Write an equation for the enrollment of Polaris High School t years after 2000. b. If this trend continues, how many students will be enrolled in 2015?