The per capita consumption (in pounds) of all poultry in a country is approximated by the function Cox)=2.74x+92.18, where x is the number of years since 2001. Find and interpret C(2), and estimate the per capita consumption of all poultry in the country in 2012
a. Find and interpret C(2).
C(2)= 97.66 (Type an integer or a decimal.)
Now interpret C(2).
The per capita consumption of poultry was __ pounds in the year__
The per capita consumption of poultry was 97.66 pounds in the year 2003.
C(2) = 97.66
Interpretation:
The per capita consumption of poultry was 97.66 pounds in the year 2003.
To find C(2), we substitute x=2 into the given function C(x)=2.74x+92.18:
C(2)=2.74(2)+92.18
C(2)=5.48+92.18
C(2)=97.66
Interpretation:
C(2) represents the per capita consumption of all poultry in the country 2 years after 2001.
Therefore, the per capita consumption of poultry was 97.66 pounds in the year 2003 (2 years after 2001).
To estimate the per capita consumption of all poultry in the country in 2012, we need to find C(x) when x represents the number of years since 2001.
Since we want to find the per capita consumption in 2012, we can subtract 2001 from 2012 to find the number of years since 2001:
2012 - 2001 = 11
So, x=11 represents the number of years since 2001 until 2012. We substitute x=11 into the given function C(x)=2.74x+92.18:
C(11)=2.74(11)+92.18
C(11)=30.14+92.18
C(11)=122.32
Therefore, we estimate that the per capita consumption of all poultry in the country in 2012 was approximately 122.32 pounds.