Math

QuestionPredict diamond production using f(x)=3.09x+148.37f(x)=-3.09 x+148.37 for 2026, where xx is years after 2017. Result: \$ \square billion.

Studdy Solution

STEP 1

Assumptions1. The function f(x)=3.09x+148.37f(x)=-3.09 x+148.37 is used to predict diamond production. . In this function, xx is the number of years after2017.
3. f(x)f(x) is the value (in billions of dollars) of the year's diamond production.

STEP 2

First, we need to find the value of xx for the year2026. We can do this by subtracting the base year (2017) from the year we are interested in (2026).
x=20262017x =2026 -2017

STEP 3

Calculate the value of xx.
x=20262017=9x =2026 -2017 =9

STEP 4

Now that we have the value of xx, we can substitute it into the function f(x)f(x) to find the predicted diamond production in2026.
f(x)=3.09x+148.37f(x) = -3.09 x +148.37

STEP 5

Substitute x=9x =9 into the function.
f(9)=3.09×9+148.37f(9) = -3.09 \times9 +148.37

STEP 6

Calculate the value of f(9)f(9).
f(9)=3.09×9+148.37=120.48f(9) = -3.09 \times9 +148.37 =120.48The diamond production in2026 is predicted to be 120.48120.48 billion.

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