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Numbers and Operations Videos 45 videos

SAT Math 1.3 Numbers and Operations
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SAT Math 1.3 Numbers and Operations. x and y must be which of the following?

SAT Math 2.4 Numbers and Operations
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SAT Math 2.4 Numbers and Operations

SAT Math 3.6 Numbers and Operations
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SAT Math 3.6 Numbers and Operations

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SAT Math 2.5 Numbers and Operations 189 Views


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Description:

SAT Math 2.5 Numbers and Operations

Language:
English Language

Transcript

00:02

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

00:08

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

00:15

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

00:21

What is Shmoopville’s annual growth rate?

00:24

And here are the potential answers...

00:26

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

00:31

of one plus some percentage growth rate…

00:34

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

00:39

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

00:43

This baby is no different. 

00:45

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

00:50

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

00:53

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

00:57

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

01:03

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

01:07

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

01:12

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

01:19

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

01:22

Now we can just solve for x.

01:23

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

01:30

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

01:37

Subtract 1 from each side and x = around 0.302.

01:42

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

01:46

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

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