Suppose the price of an item increased by 8% a total of 13 times. By what percent did the price increase in total?
Oh, I see what you're trying to do. You want to know the total percentage increase, huh? Well, let me put on my math clown hat and do some calculations.
If the price increased by 8% for 13 times, we can use the power of math to find the total percentage increase.
We'll start by raising 1.08 to the power of 13. And you know what? That gives us a whopping 2.96!
So, what does that mean? It means that the price increased by a grand total of 296% in total. Oh boy, that's quite a jump, isn't it? That item must have gotten really popular!
To find the total percent increase, we need to calculate the compound percentage increase.
Step 1: Convert the 8% increase to a decimal by dividing it by 100.
8% = 0.08
Step 2: Use the compound interest formula: Total increase = (1 + decimal increase)^number of times increased - 1
Total increase = (1 + 0.08)^13 - 1
Step 3: Calculate the total increase.
Total increase = (1.08)^13 - 1
Using a calculator, the total increase is approximately 1.156 - 1 = 0.156.
Step 4: Convert the total increase to a percentage by multiplying it by 100.
Total increase percentage = 0.156 * 100
Therefore, the price increased by approximately 15.6% in total.
To find the total percentage increase, we need to calculate the cumulative increase for each individual increase of 8% over a total of 13 times.
To do this, we will use the formula for calculating the total percentage increase:
Total Percentage Increase = 100% × (1 + Percentage Increase)^Number of Increases - 100%
In this case, the Percentage Increase is 8% and the Number of Increases is 13.
Plugging these values into the formula, we get:
Total Percentage Increase = 100% × (1 + 0.08)^13 - 100%
Simplifying this equation will give us the answer. Let's calculate it step by step:
1. Calculate the expression inside the parentheses: (1 + 0.08) = 1.08.
2. Raise 1.08 to the power of 13: 1.08^13 ≈ 2.759
3. Multiply the result by 100%: 100% × 2.759 = 275.9%
4. Subtract 100% from the result: 275.9% - 100% = 175.9%
Therefore, the price increased by approximately 175.9% in total.
1.08^13 = 2.72
That is, a 172% increase