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QUESTION 4 Which of the following graphs could be modelled using a geometric sequence? (A) © 30 25 20 t 15 10 5 - - (B) (D) 30 25 20 t 15 10 5 0 30 25 20 {15 10 - o 1 2 3 4 5 6
QUESTION 26 (5 marks) A scientist observed that the population of a specific bird species is decreasing by 17% each year and that at the beginning of 2016 there were 483 birds. a) Use a geometric sequence to model the bird population. [2 marks] b) Using the model from 26a) predict the number of birds remaining at the beginning of 2021. [3 marks]
QUESTION 14 A town’s current population of 15480 is predicted to grow steadily at an annual rate of 12%. The predicted population after 10 years is approximately (A) 48079 (B) 34056 (C) 18576 (D) 17338
QUESTION 20 (4 marks) A farmer bought a tractor for $45 100 at the start of 2012. It depreciates by $2700 each year. Identify and use a mathematical model to determine the value of the tractor at the start of 2021.
QUESTION 7 (6 marks) The table shows the total number of times a new song is played on a music service in the days following its first release. Number of days since first release Total number of times played (’000s) The songwriter is paid 0.175 cents every time their song is played and will be paid after 60 days. They predict that by that time they will be owed at least $1000. Given that the number of times the song is played is increasing exponentially evaluate the reasonableness of this prediction.
QUESTION 6 (7 marks) The first three lines in a pattern have the equations given. Their slopes form the terms of one sequence and their y-intercepts form the terms of another sequence. Each sequence is either arithmetic or geometric. Line 1: y=-0.8x + 1.2 Line2: y=0.4x+2.7 Line3: y=-0.2x+ 4.2 Determine the coordinates of the point where Line 5 in the pattern intersects Line 1.
QUESTION 6 In January 2022 40 fish were released into a new dam that has the capacity to support 10 000 fish. It is predicted that the dam will reach its capacity in January 2030 if the fish population doubles every year. Which sequence rule models the prediction? (A) ¢ =tr° ) where t = 40 r=2 n=8 (B) ¢ =t r° Y where t = 40 r= 2 n=9 (C) t =t +(n—l)d where t; = 40 d=2 n=8 (D) ¢ =t +(n—l)d where t = 40 d=2 n=9
QUESTION 15 The resale value of a boat shows geometric decay. Resale value ($) 50000 40000 32 000 Determine the resale value four years after purchase. (A) $16 000 (B) $20 480 (C) $22 000 (D) $25 600
QUESTION 10 The fourth fifth and sixth terms of a geometric sequence are 7.5 3.75 and 1.875 respectively. The sum of the first and second terms in the geometric sequence is A) 15 (B) 30 (C) 45 (D) 90
QUESTION 27 (3 marks) Use the recursive rule t .q; = 0.65t t; = 120 to complete the following. a) Calculate the percentage by which each term decreases. [1 mark] b) Calculate t4. [2 marks]
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