Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

Chris2
Member
From: Mathlifrey
Registered: 2014-04-23
Posts: 1,106
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.


Science is a way of thinking much more than it is a body of knowledge.
- Carl Sagan

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

ShivamS
Member
Registered: 2011-02-07
Posts: 3,555

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

Chooipian, your answer is right.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

Chris2
Member
From: Mathlifrey
Registered: 2014-04-23
Posts: 1,106
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?


Science is a way of thinking much more than it is a body of knowledge.
- Carl Sagan

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,423

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,423

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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

Chris2
Member
From: Mathlifrey
Registered: 2014-04-23
Posts: 1,106
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)


Science is a way of thinking much more than it is a body of knowledge.
- Carl Sagan

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,200

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB