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# This is new to me... I would like to understand more about continuously increasing something.

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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

Apr 5, 2019
edited by GAMEMASTERX40  Apr 5, 2019

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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   Apr 6, 2019
#2
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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
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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 !!!   CPhill  Apr 6, 2019
#4
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Nice! Thanks so much, this will help me a lot. -- 7H3_5H4D0W

GAMEMASTERX40  Apr 6, 2019