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