ShmoopTube

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A little birdy told us you wanted to solve a shmoopy problem...so, tweet tweet.

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The population of Shmoopville is growing exponentially. In 2009, there were 925,000 residents.

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The population is expected to increase to 1,567,000 by 2011.

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What is Shmoopville’s annual growth rate?

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And here are the potential answers...

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Okay, the big insight they're testing here is whether we get the basic formulaic concept

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of one plus some percentage growth rate…

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…that total then raised to an exponent or power which reflects the number of iterations

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we’re gonna run on that problem. And most of the time, it's years. 

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This baby is no different. 

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So, the problem gives us the base case population it's 925,000. 

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We then have to multiply it some number of times...

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...to get $1,567,000 2 years later.

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Why 2 years? Because it gives us the 2011 here and the 2009 here and, well…

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2 years pass and yeah. Babies. Lots and lots and lots of babies.

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So we can set up the equation now. The base is 925 thousand. It has to be multiplied by

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1 plus some growth rate - call it x - and THAT part's gonna get squared.

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To get the 1,567,000 number. Got it?

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Now we can just solve for x.

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We’ll need to divide both sides by 925,000…which gives us about 1.694 = (1+x) squared.

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Then we take the square root of both sides…to get 1.302…ish… = 1 + x.

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Subtract 1 from each side and x = around 0.302.

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Or, if we’re in a rounding mood… a growth rate of about 30 percent.

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The correct answer is (B). Looks like Shmoopville is quite the booming metropolis.

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