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.

GAMEMASTERX40 Apr 5, 2019

#1**0 **

For * continuous* growth..... we have this

A = A_{0}*e^(r*t)

Where A is the final number, A_{0} 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

CPhill Apr 6, 2019

#2**-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