Question
In a given country, the average price of a gallon of unleaded gasoline in 2000 was \( \$ 2.53 \). In 2016 , the average price was \( \$ 3.18 \). Find and interpret the average rate of change in the price of a gallon of gasoline per year. The average rate of change is \( \$ \square \) per year. Type an integer or a decimal. Round to the nearest cent as needed.)
Ask by Gibson Nichols. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The average rate of change in the price of a gallon of gasoline is \$0.04 per year.
Solution
To find the average rate of change in the price of a gallon of gasoline per year from 2000 to 2016, follow these steps:
1. **Calculate the Change in Price:**
\[
\text{Change in Price} = \$3.18 - \$2.53 = \$0.65
\]
2. **Calculate the Number of Years:**
\[
\text{Number of Years} = 2016 - 2000 = 16 \text{ years}
\]
3. **Determine the Average Rate of Change:**
\[
\text{Average Rate of Change} = \frac{\$0.65}{16 \text{ years}} = \$0.040625 \text{ per year}
\]
4. **Round to the Nearest Cent:**
\[
\$0.040625 \approx \$0.04 \text{ per year}
\]
**Interpretation:**
The average rate of change in the price of a gallon of gasoline is **\$0.04 per year**. This means that, on average, the price increased by 4 cents each year between 2000 and 2016.
**Answer:**
$0.04 per year
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Simplify this solution Bonus Knowledge
To find the average rate of change in the price of a gallon of gasoline from 2000 to 2016, we can use the formula: \[ \text{Average Rate of Change} = \frac{\text{Price in 2016} - \text{Price in 2000}}{\text{Year in 2016} - \text{Year in 2000}} \] Substituting the given values: \[ \text{Average Rate of Change} = \frac{3.18 - 2.53}{2016 - 2000} = \frac{0.65}{16} \approx 0.040625 \] Rounding to the nearest cent, we find that the average rate of change is approximately \( \$0.04 \) per year. So, the final answer is: The average rate of change is \( \$0.04 \) per year.
