Number of passengers of a bus company in southern Chile has been decreasing in recent years at a linear rate. In year 2015 number of passengers was 24,500 and in year 2021 number of passengers was 21,500. Consider that "x" is number of passengers and t is time (measured in years): (a) Construct Linear Function relating both variables x = f(t). b) Calculate slope value and how is interpreted? c) Calculta independent term and how is interpreted? d) What is expected number of passengers in year 2023? d) In what year will company reduce number of passengers to 50% of passengers in year 2021?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Course: Mathematical Fundamentals
Number of passengers of a bus company in southern Chile has been decreasing in recent years at a linear rate. In year 2015 number of passengers was 24,500 and in year 2021 number of passengers was 21,500. Consider that "x" is number of passengers and t is time (measured in years):
(a) Construct Linear Function relating both variables x = f(t).
b) Calculate slope value and how is interpreted?
c) Calculta independent term and how is interpreted?
d) What is expected number of passengers in year 2023?
d) In what year will company reduce number of passengers to 50% of passengers in year 2021?

Expert Solution
Step 1

Let 2015 be base year
then

f(2015)=f(0)=24500f(2021)=f(6)=21500

(a)

equation of function is given by following formula-f(t)-f(0)t-0=f(6)-f(0)6-0f(t)-24500t=21500-245006=-30006=-500f(t)=-500t+24500

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Follow-up Question

According to the previous answers, I see that independent term is number of years (t) and it is wrong because t affects variable x, and "t" are different values (2015 and 2021) as observed in statement. Please confirm your results.
And  INTERPRETATIONS about slope and independent term that are clearly requested in questions b) and c) have not been answered.

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