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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

Respuesta :

carlosego
For this case we have a function of the form:
 [tex]y = A * (b) ^ t [/tex]
 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:
 [tex]2A = A * (1,083) ^ t [/tex]
 From here, we clear t:
 [tex](1,083) ^ t = 2 log1.083 ((1.083) ^ t) = 2 t = log1.083 (2) t = 8.7 hours[/tex]
 Answer:
 it takes for the size of the sample to double about:
 [tex]t = 8.7 hours[/tex]

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