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For each problem below, solve algebraically. Then, use a table or graph to check your answer.

 

1.) A certain strain of bacteria grows continuously at a rate of 58.4% for t hours. In
approximately how many hours will 4 bacteria first increase to 2500 bacteria? Round
your answer to the nearest hour.

 Apr 5, 2019
edited by GAMEMASTERX40  Apr 5, 2019
 #1
avatar+111392 
0

For continuous growth..... we have this

 

A = A0*e^(r*t)

Where A is the final number, A0 is the original number, e = 2.718...., r =  hourly growth rate as a decimal, t = time in hours

 

So we have

 

2500 =  4 * e^(.584 t)    divide both sides by 4

 

625 =  e^(.584   t)    take the natural log, Ln, of both sides

 

Ln 625  = Ln ^(.584 t)        and by a log property, we can write

 

Ln 625  = .584t * Ln e       [ Ln e  = 1....so....we can ignore this ]

 

Ln 625  = .584 t       divide both sides by .584

 

Ln 625 / .584  = t ≈11.02 hrs = 11 hrs

 

 

cool cool cool

 Apr 6, 2019
 #2
avatar+956 
-6

Wow, that's a lot! Is there a way to check your work with a table or graph? Thanks!

 

-- 7H3_5H4D0W

GAMEMASTERX40  Apr 6, 2019
 #3
avatar+111392 
0

Look at the graph here, GM : https://www.desmos.com/calculator/g2185zbyzy

 

Note that 2500 bacteria are reached at about 11.024 hrs  = 11 hrs (rounded)

 

BTW.....as you become more familiar with this....it won't seem that daunting ....it's not as difficult as it first appears !!!

 

 

cool cool cool

CPhill  Apr 6, 2019
 #4
avatar+956 
-4

Nice! Thanks so much, this will help me a lot. laugh

 

-- 7H3_5H4D0W

GAMEMASTERX40  Apr 6, 2019

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