Question

Cheese production in a country is currently growing at a rate of 4% per year. the equation y=8.3(1.04)^× models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.

a. Estimate the total cheese production in the country in 2006

b. assuming this equation continues to be valid in the future use the equation to predict the total amount of cheese produced in the country in 2017.

Answer 1

Given the equation:
`y = 8.3(1.04)^x` ......[1]

where

y is the amount of cheese produced in billions of pounds and

x represents the number of years after 2003

Since, this equation models the cheese production in the country from 2003 to 2009.

(a)

we have to find the total cheese production in the country in 2006.

Substitute x = 3 years(i.e, 2003 -2006) in [1] to solve for y;

`y = 8.3(1.04)^(3)`

Simplify:

y = $9.3363712

Therefore, the total cheese production in the country in 2006 is, $9.34.

(b)

we use the equation to predict the total amount of cheese produced in the country in 2017.

We have x = 14 years.

Substitute in [1] we get;

`y = 8.3(1.04)^(14)`

Simplify:

y = $14.3729145151

Therefore, the estimate total amount of cheese produced in the country in 2017 is, $14.37

Answer 2

a. 9.34 billions of pounds.

b. 14.37 billions of pounds.

Explanation:

We have been given that cheese production in a country is currently growing at a rate of 4% per year. the equation
`y=8.3*(1.04)^(x)` models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.

a. To find the total cheese production in the country in 2006 we will substitute x= 3 in our given equation as 2006-2003=3.

`y=8.3*(1.04)^(3)`

`y=8.3*1.124864`

`y=9.3363712`

Therefore, the cheese production in year 2006 will be 9.34 billions of pounds.

b. To find the total cheese production in the country in 2017 we will substitute x= 14 in our given equation as 2017-2003=14.

`y=8.3*(1.04)^(14)`

`y=8.3*1.7316764476028035`

`y=14.37291451510326905`

Therefore, the cheese production in year 2017 will be 14.37 billions of pounds.