Question

a population of 200 bacteria doubles every 20 min. how many bacteria will there be after each amount of time? a) 20 min b) 60 min c) 4 h

Explanation:

Step1: Identify the growth formula

The population growth formula for doubling - time is $P = P_0\times2^{\frac{t}{d}}$, where $P_0$ is the initial population, $t$ is the time elapsed, and $d$ is the doubling - time. Here, $P_0 = 200$ and $d = 20$ minutes.

Step2: Solve for part a

When $t = 20$ minutes, substitute into the formula: $P=200\times2^{\frac{20}{20}}$.
$P = 200\times2^1=400$.

Step3: Solve for part b

First, convert 60 minutes to the number of 20 - minute intervals. Since $\frac{60}{20}=3$, then $P = 200\times2^{\frac{60}{20}}=200\times2^3$.
$P = 200\times8 = 1600$.

Step4: Solve for part c

Convert 4 hours to minutes. 4 hours = $4\times60 = 240$ minutes. Then find the number of 20 - minute intervals: $\frac{240}{20}=12$.
$P = 200\times2^{\frac{240}{20}}=200\times2^{12}$.
$2^{12}=4096$, so $P = 200\times4096 = 819200$.

Answer:

a) 400
b) 1600
c) 819200