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Name: Date: Class: Unit 3 – Modeling with Linear Functions – Quiz 1. Which scenario could be modeled by a linear function? a. the population of a city that is growing by 3% each year b. the amount of carbon in a sample that is decaying by half every 6 hours c. the number of calories burned when running at a constant speed d. the height of a rocket 6 hours after takeoff 2. Given the data set below, would a linear function be appropriate to model the relationship between x and g(x)? Explain why or why not. x g(x) 0 0.27 2 0.55 7 0.83 10 1.11 3. Given the data set below, would a linear function be appropriate to model the relationship between x and h(x)? Explain why or why not. x H(x) 0 1.44 2 3.34 7 8.09 10 10.94 4. Consider this function in recursive form. f(1) = -3 f(n) = f(n – 1) + 3; n ≥ 2 Select the equivalent explicit function for n ≥ 1. a. b. c. d. f(n) = 3(n – 1) f(n) = -3(n – 1) f(n) = n + 3 f(n) = 3n – 6 5. A theater needs to place seats in rows. The function, f(r), as shown below, can be used to determine the number of seats in each row, where r is the row number. f(1) = 8 f(r) = f(r – 1) + 3 Use the function to complete the table indicating the number of seats in each row for the first four rows of the theater. Row Number Number of Seats 1 2 3 4 6. Consider this function in explicit form. f(n) = 3n – 4; n ≥ 1 Select the equivalent recursive function. a. f(1) = -1 f(n) = f(n – 1) + 3; n ≥ 2 b. f(1) = -1 f(n) = 3f(n – 1); n ≥ 2 c. f(0) = -4 f(n) = 3f(n – 1); n ≥ 2 d. f(0) = -4 f(n) = f(n – 1) + 3; n ≥ 2 7. For the function g(x) = x2, find the average rate of change from x = 2 to x = 5. Solutions: 1. C 2. Yes, it is linear because it has a constant slope of 0.28. 3. Slope is constant at 0.95, so it is linear. 4. D Row Number Number of Seats 1 8 2 11 3 14 4 17 5. 6. A 7. (g(5) – g(2))/(5 – 2) = 7