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 108.71
pounds in the year 2006
.
Part 3
b. Estimate the per capita consumption of all poultry in the country in 2012
.
The per capita consumption in 2012
will be enter your response here
pounds.
(Type an integer or a decimal.)
Let's break down the problem step by step:
Part 1:
We have the equation for per capita consumption of poultry C(x) = 2.51x + 96.16, where x is the number of years since 2001.
a. Find C(5):
To find C(5), we substitute x with 5 in the given equation:
C(5) = 2.51 * 5 + 96.16
C(5) = 12.55 + 96.16
C(5) = 108.71
Part 2:
Now interpret C(5):
C(5) represents the per capita consumption of poultry in the year 2006 (since 2001 + 5 years = 2006). The interpretation is:
The per capita consumption of poultry was 108.71 pounds in the year 2006.
Part 3:
b. Estimate the per capita consumption of all poultry in the country in 2012:
To estimate the consumption in 2012, we need to find the value of x that corresponds to the year 2012. Since the function starts from the year 2001, the number of years since 2001 up to 2012 is 2012 - 2001, which is 11 years.
Now we calculate C(11):
C(11) = 2.51 * 11 + 96.16
C(11) = 27.61 + 96.16
C(11) = 123.77
The per capita consumption in 2012 will be approximately 123.77 pounds.