In a certain culture of bacteria, the number of bacteria increased sixfold in 10h. Assuming natural growth, how long did it take for their number to double?

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- February 25th 2010, 10:56 AMAbaloHelp with calculus problem
In a certain culture of bacteria, the number of bacteria increased sixfold in 10h. Assuming natural growth, how long did it take for their number to double?

- February 25th 2010, 11:05 AMe^(i*pi)
This is classic exponential growth so use the equation A(t) = A_0e^{kt}

where:

- = Amount at time
*t* - = Amount at time 0/initial amount
- = growth constant
- = time

By definition the amount at time 0 is equal to

If the increase is sixfold after ten hours we get the following:

which is equal to

From there you can find k

Once you know your value of k find t using the rearranged equation below and that

- = Amount at time