Exponential decline? number of farms in United States

[bailey526]

The number N of farms in the United States has declined continually since 1950. In 1950, there were 5,388,000 farms, and in 2001 that number had decreased to 2,158,000. Assuming the number of garms decreased according to the exponential model:
a. Find the value of k, and write an exponential function that descrives the number of farms after time t, in years, where t is the number of years since 1950.
b. Estimate the number of farms in 2010 and 2015.
c. At this rate of decay, in what year will less than 100,000 farms remain in the US?

 

[stapel]

The number N of farms in the United States has declined continually since 1950. In 1950, there were 5,388,000 farms, and in 2001 that number had decreased to 2,158,000. Assuming the number of garms decreased according to the exponential model:

So you know that your model will be of the form "A = Pe[sup:3n1fn9lb]kt[/sup:3n1fn9lb].

a. Find the value of k, and write an exponential function that descrives the number of farms after time t, in years, where t is the number of years since 1950.

You are given the value of P, and are given the point (t, A) = (51, 2158000). Plug this into the modelling equation and solve for the value of "k".

b. Estimate the number of farms in 2010 and 2015.

Subtract to find the number of years after t = 0 (that is, after 1950) that is represented by each date above. Plug these t-values into the modelling equation, and simplify to find the estimated numbers.

c. At this rate of decay, in what year will less than 100,000 farms remain in the US?

Plug "100000" in for "A", and solve for "t".

If you get stuck, please reply showing how far you have gotten. Thank you!