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.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)