An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the b

Question

can some one walk me through the steps to solve this problem and explain?

Answer 1

It looks that one bacteria increases in numbers at doubling every hour, which is exponential growth base 2.

The function is:  y = a (1 + r )^x, where a = initial amount, r = growth rate, x = number of interval

Therefore, y = 1 (1 + 1)^x = 2^x =  2^24 = 16,777,216

With 10 bacteria and x number of interval,

      y = 10 * 2^x = 16,777,216

take log on both side,  log (10 * 2^x) = log 16,777,216

                                 log 10+ x(log 2) = log 16,777,216  

                                 x = ( log 16,777,216 - log 10 ) / log 2 =  20.678.... 

or ,  take natural log  ln on both side and solve for x ,

                                 x = ln (1,677,721.6) / ln (2) = 20.678... (same)

It will take about 20 hours 40 min 41 sec.