1. ## Exponential Models

A culture contains 1700 bacteria initially and doubles every 30 minutes. Find a function that models the number of bacteria n(t) after t minutes. (Enter the growth rate using natural logarithm).

2. Originally Posted by cheer4life1694
A culture contains 1700 bacteria initially and doubles every 30 minutes. Find a function that models the number of bacteria n(t) after t minutes. (Enter the growth rate using natural logarithm).
$n = 1700 \cdot 2^{kt}$

$3400 = 1700 \cdot 2^{30k}$

solve for $k$ and you have your function.

or ...

$n = 1700 \cdot e^{kt}$

$3400 = 1700 \cdot e^{30k}$

solve for $k$ ... same drill.

3. ohhh ok thank you!

4. Originally Posted by cheer4life1694
A culture contains 1700 bacteria initially and doubles every 30 minutes. Find a function that models the number of bacteria n(t) after t minutes. (Enter the growth rate using natural logarithm).
Actually, a perfectly valid answer to this is $n(t)= 2^{t/30}$. Of course that does not involve entering "the growth rate using natural logarithm", but it is an exponential function that models the growth of the bacteria,