Question

1. if a population of 100 cells triples every hour, which function represents $p(t)$, the population after $t$ hours?
2. $p(t)=3(100)^t$
3. $p(t)=100(3)^t$
4. $p(t)=3t + 100$
5. $p(t)=100t + 3$

08 2017 14

Explanation:

Step1: Recall exponential growth formula

The general form of exponential growth is $p(t) = p_0(r)^t$, where $p_0$ is the initial population, $r$ is the growth factor per time period, and $t$ is time.

Step2: Identify given values

Initial population $p_0 = 100$, growth factor $r = 3$ (since the population triples each hour).

Step3: Substitute into formula

Substitute $p_0=100$ and $r=3$ into the growth formula: $p(t) = 100(3)^t$

Step4: Match with options

Compare the derived function to the provided options to find the match.

Answer:

1. $p(t) = 100(3)^t$