My Math Forum Word Problem

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 20th, 2012, 02:53 PM #1 Newbie   Joined: Nov 2011 Posts: 14 Thanks: 0 Word Problem The number of water hyacinth plants growing on a lake increases exponentially with time. On Tuesday the number of plants is 150. That Friday the number has risen to 240. If it takes 3400 plants to completely cover the lake, will the lake be completely covered by 20 days after Tuesday? Justify your answer.
February 20th, 2012, 04:12 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Word Problem

Hello, doctorbleachers!

Quote:
 The number of water hyacinth plants growing on a lake increases exponentially with time. On Tuesday the number of plants is 150.[color=beige] .[/color]That Friday the number has risen to 240. If it takes 3400 plants to completely cover the lake, [color=beige]. . [/color]will the lake be completely covered by 20 days after Tuesday? Justify your answer.

$\text{The exponential function is: }\:P \;=\;P_oe^{kt}$

$\text{Tuesday: }\:t= 0,\;P = 150$

[color=beige]. . . . . . . . [/color]$150 \:=\:P_oe^0 \;\;\;\Rightarrow\;\;\;P_o = 150$

$\text{The function (so far) is: }\:P \:=\:150e^{kt}$

$\text{Friday: }\:t= 3,\;P = 240$

[color=beige]. . . . . . .[/color]$240 \:=\:150e^{3k} \;\;\;\Rightarrow\;\;\; e^{3k} \:=\:1.6 \;\;\;\Rightarrow\;\;\; \ln\left(e^{3k}\right) \:=\:\ln(1.6) \;\;\;\Rightarrow\;\;\;3k\underbrace{\ln(e)}_{\tex t{This is 1}} \:=\:\ln(1.6)$
[color=beige]. . . . . . . .[/color]$3k \:=\:\ln(1.6) \;\;\;\Rightarrow\;\;\;k \:=\:\frac{1}{3}\,\!\ln(1.6) \:=\:0.156667876 \;\approx\;0.157$

$\text{Therefore, the function is: }\:P \;=\;150e^{0.157t}$

$\text{When will {P= 3400\,?$

[color=beige]. . [/color]$3400 \:=\:150e^{0.157t} \;\;\;\Rightarrow\;\;\;e^{0.157t} \:=\:\frac{3400}{150} \:=\:\frac{68}{3} \;\;\;\Rightarrow\;\;\;\ln\left(e^{0.157t}\right) \:=\:\ln\left(\frac{68}{3}\right) \$

[color=beige]. . [/color]$0.157t \:=\:\ln\left(\frac{68}{3}\right) \;\;\;\Rightarrow\;\;\;t \:=\:\frac{\ln\left(\frac{68}{3}\right)}{0.157} \;=\; 19.87831475\text{ days.}$

$\text{The lake will be covered in about 19 days, 21 hours.}$

 February 20th, 2012, 05:18 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 $P=150(1.6)^{t\small/3}.$ For t = 20, P = 3442.6 approximately, which exceeds 3400.
 February 20th, 2012, 08:33 PM #4 Newbie   Joined: Nov 2011 Posts: 14 Thanks: 0 Re: Word Problem Sweet. Thanks!!!

 Tags problem, word

### algebra 1 water hyacinths answer

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post angelina Elementary Math 7 August 9th, 2010 11:18 PM hemi Algebra 3 September 15th, 2009 03:48 PM Hello Elementary Math 3 September 6th, 2008 04:47 AM iReap Algebra 2 February 10th, 2008 06:37 PM chak_2007 Elementary Math 5 September 13th, 2007 04:23 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top