Question

In 1940, there were 6,102,000 farms in the United States. By 2004, the number of farms was down to 2,113,000.

a). Find the equation of the exponential function to model the number of farms after 1940.

b). Use the model to predict the number of farms in 2010.

Answer 1

Initial number of farms = 6102000

Number of farms after the years is given by

N(t) = Initial number *

=> N(t) = 6102000

For the year 2004, t = 2004 - 1940 = 64, N(t) = 2113000

Therefore



=>

=>

=> -64k = ln (2113 / 6102)

=> k = 0.01657

Therefore, the equation of exponential function is

b) For the year 2010, t = 2010 - 1940 = 70

Substituting t = 70 in N(t) we get

Number of farms in 2010

=

= 1913084