Question

The sales of a sandwich store increased approx. linearly from $52,000 to $116,000 during the first five yrs of business. Write an equation that models the sales y after x years. Determine what the sales will be at the end of 12 years if the pattern continues,

Answer 1

From x=1 to x=5
x=1 is starting time
x=time
y=mx+b
m=slope
b=yintercept

slope=(y2-y1)/(x2-x1)
for points (x1,y1) and (x2,y2)

(1,52000) and (5,116000)
slope=(116000-52000)/(5-1)=64000/4=16000
y=16000x+b
find b
(1,52000)
52000=16000(1)+b
52000=16000+b
minus 16000 from both sides
36000=b


the equation is
y=16000x+36000

at 12 years, x=12
y=16000(x)+36000
y=16000(12)+36000
y=192000+36000
y=228000

sales at year 12 is $228,000