1. ## Doubling time!

If the size of a bacteria colony doubles in 6 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

Exact:

Decimal (nearest hundreth):

ok so i know the equation that i have to use, i believe its,

2=(1+r/100)^t

and then for the tripleing time you just find, r, and plug it in...can someone let me know if im on the right track..thanks

mathlete

2. Originally Posted by mathlete
If the size of a bacteria colony doubles in 6 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.
...
Hi,

1. I assume exponential growth
2. let a be the initial amount of bacteria

With exponential growth you use the equation:

$\displaystyle A(t) = A(0) \cdot e^{k \cdot t}$ with A(t) = amount at the time t, and A(0) = initial value.

From your problem you know: A(6) = 2a

$\displaystyle 2a = a \cdot e^{k \cdot 6}~\iff~2 = e^{k \cdot 6}$$\displaystyle ~\iff~ \ln(2)= k\cdot 6~\iff~ k= \frac16 \cdot \ln(2)$

Use these results to calculate A(t) = 3a

$\displaystyle 3a = a \cdot e^{\frac16 \cdot \ln(2) \cdot t}~\iff~3 = e^{\frac16 \cdot \ln(2) \cdot t}$ $\displaystyle ~\iff~ \ln(3)= \frac16 \cdot \ln(2) \cdot t ~\iff~ t= 6 \cdot \frac{\ln(3)}{\ln(2)}$

Use a calculator to get the approximative value of $\displaystyle t \approx 9.50977... \approx 9.51$