The per capita consumption (in pounds) of all poultry in a country is approximated by the function Upper C left parenthesis x right parenthesis equals 2.51 x plus 96.16
,
where x is the number of years since 2001. Find and interpret Upper C left parenthesis 5 right parenthesis comma
and estimate the per capita consumption of all poultry in the country in 2012.
Question content area bottom
Part 1
a. Find and interpret C(5
).
C(5
)equals108.71
(Type an integer or a decimal.)
Part 2
Now interpret C(5
).
The per capita consumption of poultry was enter your response here
pounds in the year enter your response here
.
Part 1:
To find \( C(5) \), we substitute \( x = 5 \) into the given function:
\( C(x) = 2.51x + 96.16 \)
\( C(5) = 2.51(5) + 96.16 \)
\( = 12.55 + 96.16 \)
\( = 108.71 \)
So, \( C(5) = 108.71 \) pounds.
Part 2:
Interpretation:
The function \( C(x) \) represents the per capita consumption of all poultry in the country in pounds, where \( x \) is the number of years since 2001. When we calculate \( C(5) \) and get 108.71, it means that in the year \( 2001 + 5 \), or 2006, the per capita consumption of poultry was 108.71 pounds.
Now, to estimate the per capita consumption of all poultry in the country in 2012, we need to determine the value of \( x \) for that year.
Since \( x \) represents the number of years since 2001, for the year 2012, \( x = 2012 - 2001 \):
\( x = 11 \)
Now we can calculate \( C(11) \):
\( C(11) = 2.51(11) + 96.16 \)
\( C(11) = 27.61 + 96.16 \)
\( C(11) = 123.77 \)
So, the per capita consumption of all poultry in the country in 2012 was estimated to be 123.77 pounds.