Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of
8.3%
per hour. How many hours does it take for the size of the sample to double?
Note: This

Answer 1

For this case we have a function of the form:
 $y = A * (b) ^ t$
 Where,
 A: it is the initial amount of bacteria
 b: growth rate
 t: it's time
 By the time the bacteria are double we have that y = 2A
 Substituting values:
 $2A = A * (1,083) ^ t$
 From here, we clear t:
 $(1,083) ^ t = 2 log1.083 ((1.083) ^ t) = 2 t = log1.083 (2) t = 8.7 hours$
 Answer:
 it takes for the size of the sample to double about:
 $t = 8.7 hours$