Question

math and graphing tutorial
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on april 1, the price of gas at bobs corner station was $4.95 per gallon. on may 1, the price was $5.45 per gallon. on june 1, it was back down to $4.95 per gallon.
between april 1 and may 1, bobs price increased by
, or
.
between may 1 and june 1, bobs price decreased by
, or
.
suppose that at a gas station across the street, prices are always 20% higher than bobs. in absolute dollar terms, the difference between bobs prices and the prices across the street is
when gas costs $5.45 than when gas costs $4.95.
some economists blame high commodity prices (including the price of gas) on interest rates being too low.
suppose the fed raises the target for the federal funds rate from 2% to 2.75%. this change of
percentage points means that the fed raised its target by approximately
.

Explanation:

Step1: Calculate price increase from April 1 - May 1

Find the difference: $5.45 - 4.95=0.5$. Calculate percentage increase: $\frac{5.45 - 4.95}{4.95}\times100\%\approx 10.1\%$.

Step2: Calculate price decrease from May 1 - June 1

Find the difference: $5.45 - 4.95 = 0.5$. Calculate percentage decrease: $\frac{5.45 - 4.95}{5.45}\times100\%\approx9.2\%$.

Step3: Calculate price - difference between Bob's and across - the - street

When price is $4.95$, across - the - street price is $4.95\times(1 + 20\%)=4.95\times1.2 = 5.94$, difference is $5.94 - 4.95 = 0.99$. When price is $5.45$, across - the - street price is $5.45\times(1 + 20\%)=5.45\times1.2 = 6.54$, difference is $6.54 - 5.45 = 1.09$. The difference between differences is $1.09 - 0.99 = 0.1$.

Step4: Calculate change in federal funds rate

The change in percentage points is $2.75\%-2\% = 0.75$ percentage points. Calculate percentage increase: $\frac{2.75 - 2}{2}\times100\%=37.5\%$.

Answer:

Between April 1 and May 1, Bob's price increased by $\$0.5$, or approximately $10.1\%$.
Between May 1 and June 1, Bob's price decreased by $\$0.5$, or approximately $9.2\%$.
The difference between Bob's prices and the prices across the street is $\$0.1$ more when gas costs $\$5.45$ than when gas costs $\$4.95$.
The Fed raised the target by $0.75$ percentage points, which means it raised its target by approximately $37.5\%$.