Exponential growth

Question

The question is as follows:

 

Under certain conditions, the number of salmonella bacteria can increase by approximately 700% per hour.

 

Using a calculation, show that the doubling time of the number of salmonella bacteria equals 20 minutes.

Need help on how to solve this

 

 

Thank you so much!

 

Answer 1

Let N(t) = number of bacteria in t hours and let P be the initial population.

 

700% = 7.00

 

N(t) = P(1+7)^t

 

If the population doubles, then N(t) = 2P

 

So, 2P = P(8)^t

 

        2 = 8^t

 

        2 = (2³)^t

 

        2¹ = 2^3t     3t = 1

 

                          t = 1/3 hours   = 20 minutes