# Thread: Finding growth rate, from doubling time (exponential)

1. ## Finding growth rate, from doubling time (exponential)

Hi, I am a new user and need help please
Consider a certain bacterium that, once in a suitable environment, reproduces with an observed constant doubling time of 2 hours. A 15-milligram mass of the bacteria is present on the initial infection.
d) From this doubling time, calculate the rate at which the bacteria are reproducing per hour.
e) Write the formula for the model to describe the reproduction of the bacteria.

THANK YOU!! Any help is appreciated

2. ## Re: Calculating Rate from doubling time

If the bacterium starts with mass 15 mg and doubles every hour it will have mass $\displaystyle 15(2^t)$ mg after t hours. The rate of increase is the derivative of that function, $\displaystyle 16 ln(2) 2^t$ mg per hour.

3. ## Re: Finding growth rate, from doubling time (exponential)

If the bacterium starts with mass 15 mg and doubles every hour then it will have mass $\displaystyle 15(2^t)$ mg after t hours. It's "rate of reproduction" is the derivative of that, $\displaystyle 15 ln(2) 2^t$ mg per hour.

4. ## Re: Calculating Rate from doubling time

Thank You! So to get the answer for rate of production for 1 hour would i put - 15ln(2)2^1?