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What single percentage change is equivalent to a 7% increase followed by a 22% increase

User RegularGuy
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Final answer:

To calculate the equivalent single percentage increase for a 7% increase followed by a 22% increase, we compound the increases and find that 1.07 times 1.22 equals 1.306. This means the total increase is 30.6%, so the equivalent single percentage increase is also 30.6%.

Step-by-step explanation:

The student has asked what single percentage change is equivalent to a 7% increase followed by a 22% increase. To calculate this, we first need to consider the compounded effect of both percentage increases on an initial amount. Let's assume a starting value of 1 (or 100%), which represents any initial amount.

First, we apply the 7% increase:

Initial amount = 1

After 7% increase = 1 × (1 + 0.07) = 1.07

Then, we apply the 22% increase to the new amount:

Amount after first increase = 1.07

After 22% increase = 1.07 × (1 + 0.22) = 1.306

So, the final amount is 1.306 times the original amount, which corresponds to a 30.6% total increase. However, to find the single percentage growth rate equivalent to sequential increases of 7% and 22%, we use the formula for compound interest:

Equivalent single percentage increase = (Final Amount/Initial Amount - 1) × 100%

In this case, that's (1.306/1 - 1) × 100% = 30.6%

Therefore, a single percentage increase equivalent to a 7% increase followed by a 22% increase is 30.6%.

User Brice Argenson
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