Question

a type of bacterium triples every hour. there are 50 bacteria to start with. how many will there be after each number of hours? a) 3 b) 5 c) t

Explanation:

Step1: Identify the growth formula

The population of bacteria follows an exponential - growth formula $P = P_0\times r^n$, where $P_0$ is the initial population, $r$ is the growth factor, and $n$ is the number of time - intervals. Here, $P_0 = 50$, $r = 3$, and $n$ is the number of hours.

Step2: Calculate for $n = 3$

Substitute $P_0=50$, $r = 3$, and $n = 3$ into the formula $P = P_0\times r^n$.
$P=50\times3^3=50\times27 = 1350$.

Step3: Calculate for $n = 5$

Substitute $P_0 = 50$, $r = 3$, and $n = 5$ into the formula $P = P_0\times r^n$.
$P=50\times3^5=50\times243 = 12150$.

Step4: Calculate for $n = t$

Substitute $P_0 = 50$, $r = 3$, and $n = t$ into the formula $P = P_0\times r^n$.
$P = 50\times3^t$.

Answer:

a) 1350
b) 12150
c) $50\times3^t$