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%.