Question

a type of bacterium triples every hour. if there are 20 bacteria now, how many will there be after each amount of time? b) 6 h

Explanation:

Step1: Identify the growth formula

The formula for exponential - growth is $N = N_0\times r^t$, where $N_0$ is the initial amount, $r$ is the growth factor, and $t$ is the time. Here, $N_0 = 20$, $r = 3$, and $t$ is the number of hours.

Step2: Substitute the values

We want to find the number of bacteria after $t = 6$ hours. Substitute $N_0=20$, $r = 3$, and $t = 6$ into the formula $N = N_0\times r^t$. So $N=20\times3^6$.

Step3: Calculate $3^6$

$3^6=3\times3\times3\times3\times3\times3 = 729$.

Step4: Calculate the final number of bacteria

$N = 20\times729=14580$.

Answer:

14580