Question

2. In 1990, a total of $557 billion was spent on food and drinks in the U.S. In 2003, the total spent was S947 billion. (a) Find the equation of the exponential function that models the total spent on food and drinks in the U.S. As a function of the number of years since 1990. Use the model from part (a) to predict the amount spent in 2000. (b) Moody, S18 Project, 581.odt Page 1 of 3

Answer 1

(a) An exponential function f is of the form where a=initial quantity when t=0 and b is the factor by which f changes when t increases by 1 unit.

f=aぷ

In the problem let X: number of years after 1990

Y= amount spent in billions Dollar

So , we have the points (0,557) if the starting year 1990 is taken as initial point. Another point is (13, 947). Our model is therefore

y-557(b)18 947 557(b)13 11.70018 b 1.0417

Hence the exponential function becomes

y-557(1.0417)

(b) The amount spent in the year 2000 is

( here t=10).

y= 557(1.0417)10-838.07$ billion