5. The rate of change in revenue for the Priceline Group from 2004 to 2013 can be modeled

by x = 0.07e0.2387t, where R is the revenue (in billions of dollars) and t is the time in

years), with t=4 corresponding to 2004. In 2013, the revenue for the Priceline Group was

$6.8 billion.

a. Find a model for the revenue of the Priceline Group

b. Find the revenue of the Priceline Group in 2012.

a) R (x) = 0,2933*e∧0,2387*t

b) 5,9042 billions of dollars

Step-by-step explanation:

The rate of change in revenue dR/dt for Priceline Group is

dR/dt = 0,07*e∧0,2387*t

dR = (0,07*e∧0,2387*t) * dt

∫dR = ∫ (0,07*e∧0,2387*t) * dt between 2004 to 2013 (t = 4 stands for 2004 and t = 13 stands for 2013)

R (x) = (0,07 / 0,2387) * e∧0,2387*t)

R (x) = 0,2933*e∧0,2387*t

Then

R (4) = 0,2933*e∧0,2387*4

R (4) = 0,2933*2,5981

R (4) = 0,7602 billions of dollars

R (12) = R (4) + 0,2933*e∧0,2387*12

R (12) = 0,7602 + 5,1440

R (12) = 5,9042 billions of dollars