Example The growth of a colony of bacteria is provided by the equation,

                                           Q = Q e^{0.195 t}

If there are at first 500 bacteria exist and t is given in hours find out each of the following.

(a) How several bacteria are there after a half of a day?  

(b) How much time will it take before there are 10000 bacteria in the colony?  

Solution

Following is the equation for this starting amount of bacteria.

                                               Q =500 e^{0.195 t}

(a) How several bacteria are there after a half of a day?

In this case if we desire the number of bacteria after half of a day we will have to use t = 12 as t is in hours.  Thus, to obtain the answer to this part we only need to plug t into the equation.

                         Q = 500 e^0.195(12)  = 500 (10.3812365627 ) =5190.618

Thus, as a fractional population doesn't make any sense we'll say that after half of day there are 5190 of the bacteria present.

 (b) How much time will it take before there are 10000 bacteria in the colony?

Do not make the mistake of supposing that it will be approximately 1 day for this answer depends on the answer to the previous part. Along exponential growth things just don't work that way as we'll illustrate.  To answer this part we will have to solve the following exponential equation.

                                                          10000 = 500 e^{0.195 t}

Let's do that.

 10000/500  =e ^{0.195 t}

20 = e^{0.195 t}

ln 20 = ln e^{0.195 t}

 

ln 20 = 0.195t  ⇒ t = ln 20 / 0.195 =15.3627

Thus, it only takes approximately 15.4 hours to attain 10000 bacteria and not 24 hours if we only double the time from the first part. In other terms, be careful!

Posted Date: 4/8/2013 5:13:39 AM | Location : United States

Ask an Expert

Related Discussions:- Example of exponential growth, Assignment Help, Ask Question on Example of exponential growth, Get Answer, Expert's Help, Example of exponential growth Discussions

Write discussion on Example of exponential growth
Your posts are moderated

Write your message here..

Related Questions

Writing and Simplifying Algebraic Expressions, -8x+9x-13x -8x+9x-13x

Armt math blitz, what is the reciprocal of 4 over 3 . what is the reciprocal of 4 over 3 .

Negative Integer Exponents, In 1975, the U.S. Environmental protection agen... In 1975, the U.S. Environmental protection agency set a standard of 50 parts per billion of lead in drinking water. In 1991, a new standard was set that safe water contains less th

Factorisation, http://www.transtutors.com/live-online-tutor/math-help/ http://www.transtutors.com/live-online-tutor/math-help/

Adding Rational expressiona, How do I simplify x^2+2 + -(4x-2) How do I simplify x^2+2 + -(4x-2)

Function evaluation, f(x)=xsqr-1 f(x)=xsqr-1

#title2.., #questionfWRWETWE.. #questionfWRWETWE..

Two forms of the parabola, There are two forms of the parabola which we wil... There are two forms of the parabola which we will be looking at. The first form will make graphing parabolas very simple.  Unluckily, most parabolas are not in this form.  The seco

Homework, 10n+2+32 what does n equal 10n+2+32 what does n equal

Help please, Achieve $225,500 at 8.75% compounded continuously for 8 years,... Achieve $225,500 at 8.75% compounded continuously for 8 years, 155 days