In a report issued by the U.S Department of Transportation in 2020, it was predicted that the number of passengers boarding planes in the United States would grow steadily from the current 0.7 billion boardings/year to 1.2 billion boardings/year in 2032.
a. Find a linear function f giving the projected boardings (in billions) in year t, where t=0 corresponds to 2012.
b. What is the projected annual rate of growth of boarding between 2012 and 2032?
c. How many boarding per year are projected for 2022?
a. 2032-2012=20
(0,0.7) (20,1.2)
1.2-0.7/20-0= 0.5/20 = 0.025
y-1.2=0.025(x-20)
y-12=0.025x-0.5
y-1.2+1.2=0.025x-0.5+1.2
y=0.025x+0.7
f(0)=0.025(0)+0.7=0.7
b. 2032-2012=20
f(20=0.025(20)+0.7=1.2
c. 2022-2012=10
f(10)= 0.025(10)+0.7 = 0.95