Parting in the year 2000, the number of speeding tickets issued each year in Mid

Question

Parting in the year 2000, the number of speeding tickets issued each year in Middletown is predicted to grow according an exponential growth model. During the year 2000, Middletown issued 200 speeding tickets (P_0 = 200). Every year thereafter, the number of speeding tickets issued is predicted to grow by 10%. According to the model, how many speeding tickets are likely to be issued in Middletown during 10) __ 2002? A) 222 B) 220 C) 242 D) 240 E) none of these According to the model, approximately how many speeding tickets are likely to be issued in Middletown during 2025? A)1970 B) 2167 C) 450 D) 700 E) none of these According to the model, in what year will approximately 354 speeding tickets be issued in 12) ___ Middletown? A) 2005 B) 2055 C) 2006 D) 2035 E) none of these For each speeding ticket issued, Middletown charges $50. Approximately how much money did Middletown earn from speeding tickets during the time period 2000-2025? A) $541, 750 B) $21, 850 C) $108, 350 D) $300 E) $1, 091, 800

Explanation / Answer

10) YEAR 2000

P0 = 200

n = 0 --> 2000

r = 10% = 0.1

Pn denotes the number of speeding tickets during the year 2000+n

then the recursive formula Pn is

Pn = (1+r)Pn-1

So P2001 = (1.1)* 200 = 220

P2002 = (1.1)* 220 = 242

11) Now we use explicit formula = Pn = P0(1+r)n

where n = 2025-2000 = 25

Pn = 200 * (1.1)25

Pn = 2166.66 = 2167

12) 354 = Pn = 200*(1.1)n

n = 6

Ans = 2006

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