Question

a particular strain of bacteria triples in population every 15 minutes. assuming you start with 120 bacteria in a petri dish, how many bacteria will there be in 1 hour?
a. 9720
b. 6547
c. 7086
d. 4374

Explanation:

Step1: Calculate number of 15 - minute intervals in 1 hour

There are 60 minutes in 1 hour. Since each interval is 15 minutes, the number of intervals $n=\frac{60}{15}=4$.

Step2: Use the exponential - growth formula

The initial number of bacteria $a = 120$, and the bacteria triples every 15 - minute interval. The formula for the final number of bacteria $N$ is $N=a\times3^{n}$. Substitute $a = 120$ and $n = 4$ into the formula: $N=120\times3^{4}$.

Step3: Calculate $3^{4}$

$3^{4}=3\times3\times3\times3 = 81$.

Step4: Calculate the final number of bacteria

$N=120\times81=9720$.

Answer:

A. 9720