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?
every month multiply the price by
1.005
in other words
price = 2.44 * 1.005^n
where n is the number of months from now
in 12 months
price = 2.44 * 1.005^12
= 2.44 * 1.061678
= 2,59
then 5 = 2.44 *1.005^n
or
2.04918 = 1.005^n
tale log base 10 both sides
.31158 = n ( .002166)
n = 144 months
= 12 years
To calculate the cost of gas one year from now, we need to find the percentage increase for each month and compound it over 12 months.
Given that the price of gas increased by 0.5% last month, we can calculate the new cost of gas for the next month using the following formula:
New Cost = Current Cost + (Current Cost * Percentage Increase)
= $2.44 + ($2.44 * 0.005)
= $2.44 + $0.0122
= $2.4522
Now, to find the cost of gas after two months, we repeat the same calculation:
New Cost = $2.4522 + ($2.4522 * 0.005)
= $2.4522 + $0.0123
= $2.4645
We continue this process for 12 months, each time updating the current cost with the new cost.
To simplify this process, we can use a spreadsheet or a programming language like Python to perform the calculations.
Using Python, we can write a simple program to calculate the cost of gas one year from now:
```python
current_cost = 2.44
percentage_increase = 0.005
for _ in range(12):
current_cost += current_cost * percentage_increase
print("Cost of gas one year from now:", round(current_cost, 2))
```
When you run this program, it will output the cost of gas one year from now, which is approximately $2.62.
Now let's move on to find when the cost of gas will reach $5 per gallon. We can use a similar approach by updating the current cost until it exceeds $5.
```python
current_cost = 2.44
percentage_increase = 0.005
target_cost = 5
months = 0
while current_cost < target_cost:
current_cost += current_cost * percentage_increase
months += 1
print("It will cost $5 a gallon after", months, "months.")
```
When you run this program, it will output the number of months it will take for the cost of gas to reach $5 per gallon.