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#1 2014-05-29 01:07:31

Chris2
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From: Mathlifrey
Registered: 2014-04-23
Posts: 1,230
Website

Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hello, I think the answer for
http://www.mathopolis.com/questions/q.php?id=589
Have a typo.
Q : 3 years ago you had $120 in the bank. You now have $192.
If the amount of money at the end of each year increases exponentially, then how much will you have in the bank after another 7 years?
(Assume that you do not deposit or withdraw any money)

A : Start with the formula y(t) = aekt
We know y(0) = 120
⇒ 120 = ae0
⇒ a = 120

We also know y(3) = 192
⇒ 192 = 120e3k
⇒ e3k = 192 ÷ 120 = 1.6
⇒ 3k = ln(1.6) = 0.470...
⇒ k =  0.470... ÷ 3 = 0.156668...

Now we know a and k, we can write the growth function y(t) = aekt explicitly as
y(t) = 120e0.156668t

Now, we can find how much money there will be in the bank after a further 6****(isn't this 7) years by replacing t with 10:

y(10) = 120e0.156668 × 10
= 120e1.56668
= 120 × 4.79071658...
= 574.89

You will have $574.89 in the bank after a further 7 years

Sorry if I was wrong, please explain.


Love your enemies and those who persecute you. Forgive others the way God forgives you.

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#2 2014-05-29 01:11:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,475

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hi;

My #589 is about rabbits.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2014-05-29 01:26:53

ShivamS
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Registered: 2011-02-07
Posts: 3,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Chooipian, your answer is right.

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#4 2014-05-29 01:29:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,475

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hi chooipian;

Please learn to use latex.

http://www.codecogs.com/latex/eqneditor.php

And find the correct link to the question that I may edit it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2014-05-29 01:34:18

Chris2
Member
From: Mathlifrey
Registered: 2014-04-23
Posts: 1,230
Website

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

oops... http://www.mathopolis.com/questions/q.php?id=1238 How to use latex here?


Love your enemies and those who persecute you. Forgive others the way God forgives you.

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#6 2014-05-29 01:35:22

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,463

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

It is the second question not the first.

http://www.mathopolis.com/questions/q.php?id=589&site=1&ref=/algebra/exponential-growth.html&qs=589_1238_1239_2304_2305_8089_8090_8091_8092

edit:  If you put the second page link in, you get the first question.  Does that always happen or is there a bug?

and chooipian's answer is correct.  I chose answer C and was told I'm correct with that answer.

Bob

Last edited by bob bundy (2014-05-29 01:37:42)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2014-05-29 01:36:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,475

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Take what codecogs spits out and put it between

[math]Put math here.[/math]

Hi Bob;

If you put the second page link in, you get the first question.  Does that always happen or is there a bug?

Looks like a bug.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#8 2014-05-29 01:41:09

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,463

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

hmmm.  id = 1238 leads to question 2 but my screen has question 2 and id = 589.

I've not played with these questions so I've not tested this before.

maybe chooipian got directed to the wrong answer link.

Bob

Last edited by bob bundy (2014-05-29 01:42:46)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2014-05-29 02:06:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,475

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

I am getting C, so what is the problem?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#10 2014-05-29 02:15:17

Chris2
Member
From: Mathlifrey
Registered: 2014-04-23
Posts: 1,230
Website

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Now, we can find how much money there will be in the bank after a further 6 years by replacing it with 10:

It should be 7 not 6.

Last edited by Chris2 (2014-05-29 02:17:03)


Love your enemies and those who persecute you. Forgive others the way God forgives you.

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#11 2014-05-29 02:15:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,475

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

I got it! Thanks for spotting it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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