Exponential Growth

Question

The number of bacteria in a culture at the start of an experiment is 10^4.  Ten hours later that population
has increased to 10^9.  Approximate the size of the population after 15 hours from the start.

Answer 1

You have submitted several exponential growth/decay problems.  ALL of them involve an exponential function and to solve them, taking logarithms is a key step.

 

I'm just going to do one for you.

 

P(t) = P(0)•e^kt  (this k value is positive, for exp growth; would be negative, for decay)

10⁹ = 10^4•e^k(10) 

After dividing by 10⁴

ln 10⁵ = 10k  so k = (5 ln 10) / 10 = ½ln10 = 1.151292546 (I recommend retaining all of these decimal places for maximum accuracy of all intermediate calculations--rounding only at the end of a multi-step problem)

 

P(15) = 10⁴e^15k =3162 2777 0000 or 3.16 • 10¹¹

 

Please check all of these calculations, as I've worked in haste.