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The function \( f(x)=-3.57 x+147.39 \) can be used to predict diamond production. For this function, \( x \) is the number of years after 2017 , and \( f(x) \) is the value (in billions of dollars) of the year's diamond production. Use this function to predict diamond production in 2025 .

Ask by Rojas Erickson. in the United States
Jan 22,2025

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Answer

The predicted diamond production in 2025 is \$118.83 billion.

Solution

To predict the diamond production in 2025 using the given function: \[ f(x) = -3.57x + 147.39 \] where: - \( x \) is the number of years after 2017, - \( f(x) \) is the diamond production in billions of dollars. **Step 1: Determine the value of \( x \) for the year 2025.** \[ x = 2025 - 2017 = 8 \text{ years} \] **Step 2: Plug \( x = 8 \) into the function to find \( f(8) \).** \[ f(8) = -3.57 \times 8 + 147.39 \] \[ f(8) = -28.56 + 147.39 \] \[ f(8) = 118.83 \] **Conclusion:** The predicted diamond production in **2025** is **\$118.83 billion**.

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Extra Insights

To predict diamond production in 2025, we need to determine the value of \( x \) for that year. Since \( x \) represents the number of years after 2017, for 2025, \( x = 2025 - 2017 = 8 \). Now, plug in \( x = 8 \) into the function: \[ f(8) = -3.57(8) + 147.39 \] Calculating this gives: \[ f(8) = -28.56 + 147.39 = 118.83 \] Thus, the predicted diamond production in 2025 is approximately 118.83 billion dollars.

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