The number of bacteria in a culture grew from 275 to 1135 in three hours. find the amount of time needed for the number of bacteria to grow to 5000.

6.1 hours

Step-by-step explanation:

The starting number 275 is multiplied by the factor 1135/275 in 3 hours. This gives rise to the exponential model ...

... n(t) = 275·(1135/275)^(t/3)

We want to find t when n(t) = 5000. Substituting this into the equation and solving, we have ...

... 5000 = 275·(1135/275)^(t/3)

... 5000/275 = (1135/275)^(t/3) . . . . divide by 275

... log(5000/275) = (t/3)·log(1135/275) . . . . take the log

... t = 3·log(5000/275)/log(1135/275) . . . . multiply by the inverse of the x-coefficient

... t ≈ 6.13795 . . . hours

Rounded to reasonable precision, the time is approximately 6.1 hours.

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step-by-step explanation:

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