Question

in a lab experiment, a population of 100 bacteria is able to quadruple every hour. which equation matches the number of bacteria in the population after 4 hours? answer $b = 100(1 + 4)^4$ $b = 4(100)(100)(100)(100)$ $b = 4(100)^4$ $b = 100(4)^4$

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth where the quantity multiplies by a factor each period is $P(t) = P_0(r)^t$, where $P_0$ is the initial population, $r$ is the growth factor per period, and $t$ is the number of periods.

Step2: Identify given values

Initial population $P_0 = 100$, growth factor $r = 4$ (quadruples each hour), time $t = 4$ hours.

Step3: Substitute values into formula

Substitute $P_0=100$, $r=4$, $t=4$ into the formula: $B = 100(4)^4$.

Step4: Eliminate incorrect options

• $B = 100(1 + 4)^4$ uses the compound interest formula for percentage growth, not quadrupling.
• $B = 4(100)(100)(100)(100)$ incorrectly multiplies the initial population repeatedly instead of applying the growth factor.
• $B = 4(100)^4$ misapplies the growth factor to the power of the initial population, not the time.

Answer:

$B = 100(4)^4$