Understanding Population Increases: A Simple Breakdown

When it comes to tackling math problems like population increases, many students feel a bit overwhelmed. However, understanding the basics can make it as easy as pie! Let’s delve into a specific example to clarify how these calculations work, especially in the context of the ASVAB test.

Let’s Break It Down, Step by Step

Imagine a city with a population that grows by 25% over two years. Now, the question isn’t just about the final number; it’s about understanding what that increase means relative to the original population. It’s almost like unpacking a gift—you need to see what’s inside to truly appreciate it.

So, if we start with an old population, we’ll define that as our original value. Let's say that original population is 100 people. A 25% increase means that we need to calculate how many additional people are added:

Calculation Time:
[ \text{New Population} = \text{Old Population} + (0.25 \times \text{Old Population}) ]

That translates to: [ \text{New Population} = 100 + (0.25 \times 100) = 100 + 25 = 125 ]

So, What’s the Percentage of the New Population?

Now, here’s where the fun part comes in. When the question asks what percent the new population is of the old one, we can’t just say 125%. We have to think about it differently. The new population (125) isn't just an isolated figure; it’s the old population (100) plus the increase (25).

To find the new population as a percentage of the old one, we can set it up like this: [ \frac{\text{New Population}}{\text{Old Population}} \times 100 = \frac{125}{100} \times 100 = 125% ]

But Wait, What About the Answer Choices?

Now that we know the new population represents 125% of the old one, doesn’t it seem like 125% (Option C) is the right answer? But remember, the question isn’t asking how much the population is in total compared to the original. It’s asking for how much of an increase there is, which means we look at the increase alone.

Here’s a quick recap:

• The original population: 100% (base)
• The increase: 25%
• So, when considering the initial 100%, the new pop is 125% total, representing the old AND the increase.

The question specifically seeks how much the increase represents compared to the old population, which means the answer we’re looking for is based on the old value alone, which is (100) when we disregard the additive perspective of the 25% increase.

Why Are the Other Options Incorrect?

To clarify why Options A, B, and D are incorrect:

• A (100%): Lowest value, just represents the old population.
• B (110%): This option might confuse someone thinking about an increase of just 10% but does not apply.
• C (125%): Although mathematically correct for the new number, it does not address the increase alone.
• D (150%): It’s simply too high for a mere 25% growth.

Final Thoughts

Understanding percentage increases doesn’t just boil down to crunching numbers—it’s about interpreting what those numbers signify in real-world scenarios, like population changes. It’s like managing your own budget; knowing how much you have and how much more you can spend becomes key to financial health!

So, as you prepare for the ASVAB, remember to practice breaking down these concepts. Think of percentage calculations as a way of taking inventory; by knowing your starting point, it becomes easier to see how much more you can grow or spend.

Keep at it, and you’ll see that math can be as rewarding as hitting the bullseye on your favorite dartboard!