Question

in a lab experiment, a population of 400 bacteria is able to triple every hour. which equation matches the number of bacteria in the population after 3 hours?
answer
\\( b = 400(3) \\)
\\( b = 3(1 + 400)^3 \\)
\\( b = 3(400)(400)(400) \\)
\\( b = 400(3)^3 \\)

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth where a quantity multiplies by a factor over time is $B = P(r)^t$, where $P$ is the initial population, $r$ is the growth factor per period, and $t$ is the number of periods.

Step2: Identify given values

Initial population $P=400$, growth factor $r=3$, time $t=3$ hours.

Step3: Substitute values into formula

Substitute $P=400$, $r=3$, $t=3$ into the formula: $B = 400(3)^3$

Answer:

$B = 400(3)^3$