Question

the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent

Answer 1

Given:

`\begin{gathered} P_{\text{today}}=2.92,P_(today)=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_(yesterday)=Price\text{ of a gallon of unleaded gas today} \end{gathered}`

To Determine: The percentage increase round to the nearest 1oth of a percent

The formula for percentage increase is given below:

`\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}*100\% \\ In\text{crease}=P_(final)-P_{in\text{itial}} \end{gathered}`

Substitute the given into the formula

`\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}`
`\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}*100\% \\ P_{in\text{crease}}=(0.07)/(2.85)*100\% \\ P_{in\text{crease}}=0.02456*100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}`

Hence, the percentage increase to the nearest 10th of a percent is 2.5%