Thread: More Exponential Models

The count in a culture of bacteria was 600 after 2 hours and 38,400 after 6 hours. Find a function that models the number of bacteria n (t) after t hours.

Originally Posted by cheer4life1694

The count in a culture of bacteria was 600 after 2 hours and 38,400 after 6 hours. Find a function that models the number of bacteria n (t) after t hours.

let A = number of bacteria at t = 0

$\displaystyle 38400 = Ae^{6k}$

$\displaystyle 600 = Ae^{2k}$

divide the first equation by the second ...

$\displaystyle 64 = e^{4k}$

solve for k, then go back to either equation and determine A.