Question

if a colony of bacteria starts with 1 bacterium and doubles in number every 10 minutes, how many bacteria will the colony contain at the end of 16 hours? the number of bacteria in the colony after 16 hours is (type your answer using exponential notation.)

Explanation:

Step1: Convert 16 hours to minutes

16 hours = 16×60 = 960 minutes

Step2: Calculate the number of 10 - minute intervals

Number of intervals $n=\frac{960}{10}=96$

Step3: Use the exponential - growth formula

The initial number of bacteria $a = 1$, and the bacteria double each time, so the number of bacteria $N$ after $n$ intervals is given by the formula $N=a\times2^{n}$. Substituting $a = 1$ and $n = 96$, we get $N = 2^{96}$

Answer:

$2^{96}$