The price of gas went up by 0.5% last month. Suppose gas currently costs $2.44 a gallon. If the price of gas continues to increase at this rate... What will it cost one year from now? When will it cost $5 a gallon.
To calculate the cost of gas one year from now, we need to find the amount of increase over 12 months, assuming a consistent rate of 0.5% per month.
First, let's find the monthly price increase:
Monthly increase = 0.5% * $2.44 = $0.0122
To find the cost of gas one year from now, we need to multiply the monthly increase by 12 (since there are 12 months in a year):
Total increase after 12 months = $0.0122 * 12 = $0.1464
To calculate the cost of gas one year from now, we add the total increase to the current price of $2.44:
Cost of gas one year from now = $2.44 + $0.1464 = $2.5864
Therefore, gas will cost approximately $2.59 per gallon one year from now.
Now let's calculate when the price of gas will reach $5 per gallon:
To find the number of months it takes for the price to reach $5, we need to divide the price difference by the monthly increase:
Number of months = ($5 - $2.44) / $0.0122
Now, let's calculate this:
Number of months = $2.56 / $0.0122 ≈ 209.84
Since we can't have a fraction of a month, we'll round up to the nearest whole number. Therefore, it will take approximately 210 months for gas to reach $5 per gallon.
Keep in mind that these calculations assume the price will continue to increase at a consistent rate of 0.5% per month, which may not be accurate in reality.
To calculate the cost of gas one year from now, we need to consider the 0.5% increase every month for a total of twelve months.
Step 1: Calculate the monthly increase.
Monthly increase = $2.44 x 0.5% = $0.0122
Step 2: Calculate the cost after one month.
Cost after one month = $2.44 + $0.0122 = $2.4522
Step 3: Calculate the cost after two months.
Cost after two months = $2.4522 + $0.0122 = $2.4644
Step 4: Repeat this process for twelve months.
Cost after twelve months = $2.44 + ($0.0122 x 12) = $2.44 + $0.1464 = $2.5864
Therefore, the cost of gas one year from now is estimated to be $2.5864 per gallon.
Now let's find out when the cost will reach $5 per gallon.
Step 1: Calculate the increase required to reach $5.
Increase required = $5 - $2.44 = $2.56
Step 2: Divide the increase required by the monthly increase.
Months to reach $5 = $2.56 / $0.0122 ≈ 209.84
Therefore, it will take approximately 210 months, or about 17.5 years, for the cost of gas to reach $5 per gallon.
in one year, 2.44 * 1.005^12
In n months, it will cost $5.00, when
2.44*1.005^n = 5.00