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In 2011, there wer 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 2011. How many cell phone subscribers were in Centerville in 2020 ?

1 Answer

2 votes

Answer:

43,872 subscribers

Explanation:

There's probably a formula for this, but it's only a span of 9 years so it's easy enough to just use brute force.

285 subscribers in 2011, and if that went up by 75% when they were counted again in 2012, how many MORE customers is that?

0.75(285) = 213.75 more customers in 2012

(Remember to turn the percentage into a decimal by dividing by 100.)

But we don't talk about fractions of a customer, do we? So if it were me I'd round that down to 213.

But how many total are there in 2012? We just have to add back in the original 285:

285 in 2011 + 213 more = 498 in 2012

So we could do that two-step process until we get to 2020, but there's a bit of an easier way:

  • We started with 285.
  • Then we added 0.75 of 285.
  • So that looks like this:
  • 285 + 0.75·285
  • That "285" in both terms means we ought to be able to factor it out, right? How about this:
  • (1 + 0.75)285
  • Is that the same thing? It is. Simplify:
  • 1.75 x 285 = 498 customers in 2012. Same answer.

So here's where it gets fun:

In your calculator, put 1.75 x 285, and hit "equals." You'll get 498.75.

HIT "EQUALS" AGAIN. Don't do anything else.

If yours is like most calculators, you'll get 872.8.

(If you get 116,487, clear and put the numbers in the other way: 285 x 1.75.)

What's happening is that your calculator is remembering the 1.75 term, and each time you hit "equals" it's multiplying that by the last answer you got. It's really cool when you figure it out.

But you first have to understand the "1.75 times the original number" thing, or this equation:

1.75x

Then whatever you put in for x, when you calculate it once you'll get 175% of that. When you calculate it again, you'll get 175% of that answer. Then it's just a matter of hitting "equals" 9 times until you get up to 2020.

It looks like this:

2012 - 498 customers

2013 - 872

2014 - 1527

2015 - 2673

2016 - 4677

2017 - 8186

2018 - 14,325

2019 - 25.069

2020 - 43,872 customers

See how quickly it grew? 75% Is an astonishing growth rate, and highly improbable in this scenario.

So yeah, I know there's an equation for it, but don't be afraid to just use the power of your calculator. After realizing what the calculation should be, it took me just 6 seconds to enter 1.75 x 285 into my calculator and hit "equals" 9 times. Count up the years on your fingers each time you hit "equals," and stop when you get to 2020.

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