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# Quadratic and exponential word problems — Basic example

Watch Sal work through a basic Quadratic and exponential word problem.

## Want to join the conversation?

• I don't get where you got 0.97 from. How you get it?
• Whenever it says, for example, a discount for 3% or decreases by 3%, you are always going to subtract 100% - 3%= 97%. => 0.97(when you multiply). If it says there is a 6% sales tax or there is an increase in 6% you will add that to 100%. 100+6= 106% which then you move the decimal point back two to give you 1.06 .This is where choice A comes from; they added the percents instead of subtracting. but in percents if it says 3% of 5 dollars this is where you just multiply 0.03 x 5.
• uuh this new SAT is not any easier though
• Fortunately for you, the newest version of the SAT is actually much much more simpler ( my own opinion of course) and the entire math section you can do WITHOUT a calculator. No i didn't try it, but I got a look at the new version, and saw the simplicity.
• Why is the 3% = 0.97? I thought it was 0.03
• The story is that the company is `losing` 3% per year, and we have to find how many `remain`. So if 3% are lost, 97% remain, right? That is why we use 0.97. We don't directly care about how fast the unhappy customers are piling up; instead, we want to know how many customers stay with the cable company.
• For anyone struggling with the intuition behind this problem, take a look at this video on Compound Interest: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/compound-interest-tutorial/v/introduction-to-compound-interest. I have seen many people on the forum asking the same things (e.g. why the 0.97?) and thought this could be helpful for them.
• Actually, Sir Instead of increasing the power (degree) of (0.97) it could get reduced to 0.94 by subtracting 3% ? That could also reduce the followers ?
(1 vote)
• If I understand you correctly, you would propose subtracting from the rate every year? Yes, that would also be a way of reducing the followers, but does it reduce them at the proper rate for this scenario? Let's see:
`year amount if 2(.97)^t amount by subtracting 3% each year and multiplying by original amt`
` 1 1.94 M 1.94 M `
` 2 1.882 M 1.880 M ` pretty close
` 3 1.825 M 1.820 M `
` 4 1.771 M 1.760 M `
` 5 1.718 M 1.700 M ` this version is quite a bit less
` 6 1.666 M 1.640 M `
` 7 1.616 M 1.580 M `
So, the answer is that it would be a `rough estimate`, but by 7 years, it would be 35,966 lost subscribers away from the correct number.
• At t=2 years, wouldn't the cable company lose another 3% of the subscribers(from the remaining subs after the first year)?
• Yes, exactly right. In the second year, they start with 97% of what they had the first year and lose customers all year. At the end of the second year, they have 97% of 97% of what they started with in the beginning. The short way of writing this is 2 million ∙ (0.97)²
So to calculate for ANY number of years at this loss rate, we use 2(0.97)ᵀ millions
where T is the number of year of miserable service.
• how did u know 3% is equal to 0.97?
• Lemme show you with an example,
Assume you have a bar of chocolate which is 100g (like 100%) , So if you eat 3% (which is 3g)of the chocolate you have 97%(which is 97g) left i.e, you have retained 97%;
100-3=97
This just gives you a vague idea of understanding the concept.
(1 vote)
• can i ask why the second one S(t) is not equal to the fourth one ，　it got both of same number and it would decrease it same ?
(1 vote)
• In the second one t is an exponent, in the fourth it's just a regular variable.