In 2008 Amtrak had 287 million passengers and in 2012 it had

In 2008 Amtrak had 28.7 million passengers, and in 2012 it had a record 31.2 million passengers.

a) find a linear fuction P(x)= ax+b that models the number of paddengers in millions x years after 2008.

b) Interpret the slope of the graph of y= P(x).

c) Use P(x) to estimate the number of passengers in 2014.

d) Assuming trends continue, predict when Amtrak might have 35 million passenger.

in 2008 passengers are 28.7 million

and 2012 passengers are 31.2 million

lets take 2008 = 0 years

so, 2012 = 4

so we have two points (0,28.7) and (4,31.2)

slope = 31.2 - 28.7 / 4-0 = 5/8 = .625

hence, equation P(x) = 5/8x + 28.7

c) P(x) in 2014

plug x = 6

P(x) = 5/8 (6) + 28.7 = 32.45 million

d) time when Amtrak have 35 million passengers

plug P(x) = 35

35 = 5/8(x) + 28.7

solving for x

(35 - 28.7 )* 8 / 5 = x

x = 10 approx

hence in 2018 Amtrak will have 35 million passengers