Bio diesel table problem

[donayre21]

years: 2003 2004 2005 2006 2007 2008 2009
%growth: -12.5 92.9 237 186.6 37.2 -11.7 7.3

a)According to the US Department of Energy,the US consumed 91 million gallons of biodiesel in 2005.Approximately how much biodiesel(in millions of gallons) did the US consume in 2006?In 2007?

I have been stuck in this problem for a while,what I understand so far is that I have to find the y intercept for the year 2006 and 2007 based on the information from the year 2005 which in that period the US consumed 91million gallons.I have tried doing the rise over run formula setting the m(slope) equals 237 and following the usual y2-y1/x2-x1 it did not seem to work.TO my understanding it has to do with something about exponential growth and decay.Can someone please try to do their best to explain to me how to properly execute this problem.Thank you and I look forward for a reply.

 

[stapel]

You posted this to "Calculus", rather than to either of the "algebra" categories, so presumably you are in a calculus course. What techniques did your textbook use when showing similar worked examples in the section from which this exercise came?

years: 2003 2004 2005 2006 2007 2008 2009
%growth: -12.5 92.9 237 186.6 37.2 -11.7 7.3

a)According to the US Department of Energy,the US consumed 91 million gallons of biodiesel in 2005.Approximately how much biodiesel(in millions of gallons) did the US consume in 2006?In 2007?

Not knowing how you're expected to use calculus techniques (perhaps integration, or at least summation?) for this, I can only note that you are given an initial value (for 2005) and growth factors (percentages) for other years. From this, using the simple techniques you learned back in pre-algebra for working with "percent of" word problems, you can find numerical values for the following years: just do the one-step multiplication.

what I understand so far is...
I have tried doing the rise over run formula...
TO my understanding it has to do with something about exponential growth and decay...

What does exponential growth have to do with straight-line slopes? Please provide a complete listing of what all you "have tried doing", along with a clear statement of your "understanding" of this exercise, including which techniques of calculus you believe you are expected to apply. Thank you.

 

[donayre21]

You posted this to "Calculus", rather than to either of the "algebra" categories, so presumably you are in a calculus course. What techniques did your textbook use when showing similar worked examples in the section from which this exercise came?


Not knowing how you're expected to use calculus techniques (perhaps integration, or at least summation?) for this, I can only note that you are given an initial value (for 2005) and growth factors (percentages) for other years. From this, using the simple techniques you learned back in pre-algebra for working with "percent of" word problems, you can find numerical values for the following years: just do the one-step multiplication.


What does exponential growth have to do with straight-line slopes? Please provide a complete listing of what all you "have tried doing", along with a clear statement of your "understanding" of this exercise, including which techniques of calculus you believe you are expected to apply. Thank you.

The main reason why I assumed it had to do with exponential growth is due to the fact that the entire chapter which is based around this types of problems deals with "exponential growth and decay".In previous problems they have used the following equations: P(a)^t or P(e)^-kt as well as the half life. This is a calculus class but they start out with a pre-calculus questions to refresh your mind,this is one of them.The answer for the year 2006 according to the book is 261 million gallons,I just want to know what kind of processes they used to get that answer.

 

[stapel]

The main reason why I assumed it had to do with exponential growth is due to the fact that the entire chapter which is based around this types of problems deals with "exponential growth and decay".

Okay. Then by what reasoning were you trying to find straight-line-equation info like slopes? What are you doing?

In previous problems they have used the following equations: P(a)^t or P(e)^-kt as well as the half life.

Do you understand these equations? Do you understand "half-life"?

I just want to know what kind of processes they used to get that answer.

What did you get when you applied the pre-algebra process I outlined previously?

 

[donayre21]

Okay. Then by what reasoning were you trying to find straight-line-equation info like slopes? What are you doing?


Do you understand these equations? Do you understand "half-life"?


What did you get when you applied the pre-algebra process I outlined previously?

I'm sorry but I'm still confused will you be kind enough to walk me through it?I have tried what you told me but I keep getting different answers.:|

 

[JeffM]

years: 2003 2004 2005 2006 2007 2008 2009
%growth: -12.5 92.9 237 186.6 37.2 -11.7 7.3

a)According to the US Department of Energy,the US consumed 91 million gallons of biodiesel in 2005.Approximately how much biodiesel(in millions of gallons) did the US consume in 2006?In 2007?

I have been stuck in this problem for a while,what I understand so far is that I have to find the y intercept for the year 2006 and 2007 based on the information from the year 2005 which in that period the US consumed 91million gallons.I have tried doing the rise over run formula setting the m(slope) equals 237 and following the usual y2-y1/x2-x1 it did not seem to work.TO my understanding it has to do with something about exponential growth and decay.Can someone please try to do their best to explain to me how to properly execute this problem.Thank you and I look forward for a reply.

Stapel explained it way back in her first post. This is a percentage problem that you covered in arithmetic. Slope, exponentials, half-life, etc. have nothing to do with it.

You are given the percentage change between years, correct?

If I gave you the amount consumed for one year and the percentage change between that year and the preceding (or succeeding) year, how would you find the amount consumed in the preceding or succeeding year? FORGET CALCULUS AND EVEN ALGEBRA. If the amount consumed in one year is 90 and the rate of change between that year and the next is +10%, how much is consumed in the next year?

So are you given the amount consumed in any year? If so, can you calculate the amount consumed in some other years?

 

[donayre21]

Stapel explained it way back in her first post. This is a percentage problem that you covered in arithmetic. Slope, exponentials, half-life, etc. have nothing to do with it.

You are given the percentage change between years, correct?

If I gave you the amount consumed for one year and the percentage change between that year and the preceding (or succeeding) year, how would you find the amount consumed in the preceding or succeeding year? FORGET CALCULUS AND EVEN ALGEBRA. If the amount consumed in one year is 90 and the rate of change between that year and the next is +10%, how much is consumed in the next year?

So are you given the amount consumed in any year? If so, can you calculate the amount consumed in some other years?

I know that I'm find the amount consumed in the upcoming year,I just don't get HOW THEY GOT 261!!! as the answer.I can't really learn by just instructions I need an example just as any good teacher would do.

 

[JeffM]

I know that I'm find the amount consumed in the upcoming year,I just don't get HOW THEY GOT 261!!! as the answer.I can't really learn by just instructions I need an example just as any good teacher would do.

In 2005, 91 million was consumed, right?

US consumed 91 million gallons of biodiesel in 2005

The percentage change from 2005 to 2006 was 186.6%, correct?

years: 2003 2004 2005 2006 2007 2008 2009
%growth: -12.5 92.9 237 186.6 37.2 -11.7 7.3

\(\displaystyle 1.866 * 91 \approx 170 \implies 91 + 170 = 261 \approx 91 * 2.866 = 91 * (1 + 1.866).\) Two ways to do percentages.

I am not being sarcastic: if you need someone to give you numerical examples on how to do percentages, you are not ready for calculus. Maybe a course in college algebra first.

 

[stapel]

I can't really learn by just instructions I need an example just as any good teacher would do.

And your book showed examples, and you studied loads of examples back when you learned this in pre-algebra, and then again when you reviewed it in algebra. The link (provided to you in the first reply) also showed loads of worked examples. And a quick Google search provides a whole long listing of other pages with even more worked examples. So one more "an example" obviously isn't the issue.

We really can't help you get un-stuck until we have some idea where you're stuck. Even if we could teach classes here (and we can't), the classes you've already had apparently haven't helped. So now something else is needed.

For a start, where are you having difficulty in the one-step multiplication? Or are you needing to go further back, and re-learn decimals and percents? Or something else?

I have tried what you told me but I keep getting different answers

Great! Show us what you did. Thank you!

 

[donayre21]

In 2005, 91 million was consumed, right?

The percentage change from 2005 to 2006 was 186.6%, correct?

\(\displaystyle 1.866 * 91 \approx 170 \implies 91 + 170 = 261 \approx 91 * 2.866 = 91 * (1 + 1.866).\) Two ways to do percentages.

I am not being sarcastic: if you need someone to give you numerical examples on how to do percentages, you are not ready for calculus. Maybe a course in college algebra first.

It's not that I need a semester of college algebra,I have practiced enough to understand the concepts.The main reason why I became confuse is because you gave me an example which was different than the problem asked with no answer and the other person who was replying to my post and you kept on asking me questions that made me become disoriented from the problem.I know that it had nothing to do with exponential growth or decay once Stapel cleared it up.I would have applied the algebra concept in this case if it had been a constant slope but in this case it had different slopes which is were I became confuse and asking me questions such as "Do you understand these equations? Do you understand "half-life"?" or trowing back my main question at me "So are you given the amount consumed in any year? If so, can you calculate the amount consumed in some other years?" did not help at all.A student is asking this types of question himself and trying to find the answer to the problem,that is his main goal right?Thank you for the help and I hope my feed back can help you guys understand in what position a student is when confronting this types of problems.I do apologize if at any moment I came forward as sounding rude.

 

[JeffM]

It's not that I need a semester of college algebra,I have practiced enough to understand the concepts.The main reason why I became confuse is because you gave me an example which was different than the problem asked with no answer and the other person who was replying to my post and you kept on asking me questions that made me become disoriented from the problem.I know that it had nothing to do with exponential growth or decay once Stapel cleared it up.I would have applied the algebra concept in this case if it had been a constant slope but in this case it had different slopes which is were I became confuse and asking me questions such as "Do you understand these equations? Do you understand "half-life"?" or trowing back my main question at me "So are you given the amount consumed in any year? If so, can you calculate the amount consumed in some other years?" did not help at all.A student is asking this types of question himself and trying to find the answer to the problem,that is his main goal right?Thank you for the help and I hope my feed back can help you guys understand in what position a student is when confronting this types of problems.I do apologize if at any moment I came forward as sounding rude.

I did not find you to be particularly rude. You were frustrated, and I'm a big enough boy to be able to cope with others' frustrations (usually). But if you are not able to find for yourself what a 10% increase over 90 is, that means you are missing basic mathematical information, and calculus will be a terrible ordeal for you. Furthermore, if we give you answers but not understanding, what will you do on the test when we are not around to help. The questions that we ask are the kinds of question you must learn to ask yourself.