Question

The function f(x)=0.21x + 13.8 can be used to predict diamond production. For this function, x is the number of years after 2000, and f(x) is the value in billions of dollars) of the year's diamond production. Use this function to predict diamond production in 2006. The diamond production in 2006 is predicted to be $billion. (Type an integer or a decimal.) Enter your answer in the answer box ?​

Answer 1

`\boxed {\boxed {\sf \$15.06 \ billion }}`

Explanation:

We are given the function f(x). This is the value of diamond production for the year in billions.

`f(x)= 0.21x+13.8`

We want to find the value of the diamond production in 2006.

We know that x is the number of years after 2000. The year 2006 was 6 years after 2000 because 2006 - 2000 = 6. Therefore, x (years after 2000) is equal to 6. We can substitute 6 in for x.

`f(6)= 0.21(6)+ 13.8`

Solve according to PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Multiply 0.21 and 6.

`f(6)= 1.26+13.8`

Add 1.26 and 13.8

`f(6)=15.06`

Remember the answer is in billions of dollars.

`f(6)= \$ 15.06 \ billion`

Diamond production in 2006 is expected to be worth 15.06 billion dollars.