SOLUTION: I really need HELP!! Th"e number of acres of farmland in the US has decreased from 945 million acres in 2000 to 932 million acres in 2006. Assume the number of acres of farmland

Question 302122: I really need HELP!!
Th"e number of acres of farmland in the US has decreased from 945 million acres in 2000 to 932 million acres in 2006. Assume the number of acres of farmland is decreasing exponentially.
a) Find the value k, and write an equation for an exponential function that can predict the number of acres of US farmland "t" years after 2000.
b) Predict the number of acres of farmland in 2015.
c) In what year (theorectically) will there be only 800 million acres of US farmland remaining?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The number of acres of farmland in the US has decreased from 945 million acres in 2000 to 932 million acres in 2006. Assume the number of acres of farmland is decreasing exponentially.
Form: y = ab^x
Given Points (0,945 million), (6,932 million)
----
a) Find the value k, and write an equation for an exponential function that can predict the number of acres of US farmland "t" years after 2000.
Usint the two points you get two equations:
932 = ab^6
945 = ab^0
---
From the 2nd equation you get a = 945 million
---
Substitute into the 1st equation to get:
932 = 945*b^6
b^6 = 0.9862
b = 0.9977
-----
Equation:
f(x) = (945 million)(0.9977)^x
======================================

b) Predict the number of acres of farmland in 2015.
f(15) = (945 million)(0.9977)^15 = 912.83 million
=======================

c) In what year (theorectically) will there be only 800 million acres of US farmland remaining?
800 million = 945 mill(0.9977)^x
0.8466 = 0.9977^x
x = log(0.8466)/log(0.9977)
x = 72.34
---
Year = 2000 = 72.34 = 2073
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Cheers,
Stan H.
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