Answer:
A)
B) 89.157 million tons.
C) In year 2017.
Step-by-step explanation:
We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.
A). We know that a continuous growth function is in form , where,
a = Initial value,
k = Growth rate in decimal form.
Upon substituting our given values, we will get:
Therefore, our required function would be , where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.
B) To find the world poultry production in the year 2013, we will substitute in above formula as:
Therefore, the world poultry production in the year 2013 would be 89.157 million tons.
C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:
Divide both sides by 77.2:
Take natural log of both sides:
Divide both sides by 0.016:
Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.