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Question 556139: As demand has grown, worldwide production of small cars rose from 14.5 million in 2002 to 19 million in 2007. Let a(t) represent the number of small cars produced t years after 2000. Find a linear function that fits the data. Use the function from part a to predict the number of small cars produced in 2013. In what year will 25 million small cars be produced?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! As demand has grown, worldwide production of small cars rose from 14.5 million in 2002 to 19 million in 2007. Let a(t) represent the number of small cars produced t years after 2000. Find a linear function that fits the data. Use the function from part a to predict the number of small cars produced in 2013. In what year will 25 million small cars be produced?
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Since this is a linear function use the standard form of a straight line: a(t)=mt+b, m=slope, b=y-intercept. Let 2000=year zero(t=0)
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slope, m=(19-14.5)/(2007-2005)=4.5/5=.9 (millions of cars produced per year)
Equation: a(t)=.9t+b
b=1.8 (y-intercept at year 2000)
Equation: a(t)=.9t+1.8
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small cars produced in 2013, t=11
a(11)=.9*11+1.8=11.7 million
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Year 25 million small cars will be produced
a(t)=.9t+1.8
25=.9t+1.8
.9t=25-1.8=23.2
t=23.2/.9≈28
year=2028-2=2026
ans:
small cars produced in 2013=11.7 million
Year 25 million small cars will be produced: 2026
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