Example of exponential growth, Algebra

Assignment Help:

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

                                           Q = Q e0.195 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 e0.195 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 e0.195(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 e0.195 t

Let's do that.

 10000/500  =e 0.195 t

20 = e0.195 t

ln 20 = ln e0.195 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!


Related Discussions:- Example of exponential growth

D=rt word problem solver!, Carl and his dad I stonecarvers. Carl can cut th...

Carl and his dad I stonecarvers. Carl can cut the stone in five days. With his father''s help he can carve it in two days. How long would take his father to carve it alone. Bob c

Find out the compound interest, Example: We are investing $100,000 in an ac...

Example: We are investing $100,000 in an account that earns interest at a rate of 7.5% for 54 months.  Find out how much money will be in the account if, (a) Interest is comp

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

..addition, what is 300000000000000000000+612222

what is 300000000000000000000+612222

Word problem, Can you help solve this word problem? christine collected som...

Can you help solve this word problem? christine collected some toys for charity. She donated 3/4 of the toys to charity A. then she donated 1/3 of the remaining toys to charity B.

Evaluate log function, Example    Evaluate log 5 7 . Solution At f...

Example    Evaluate log 5 7 . Solution At first, notice that we can't employ the similar method to do this evaluation which we did in the first set of instance. It would n

Math, how do you do scientific notation

how do you do scientific notation

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd