Question

in a lab experiment, a population of 100 bacteria is able to double every hour. which equation matches the number of bacteria in the population after 3 hours?
answer
○ (b = 100(2)^3)
○ (b = 2(100)^3)
○ (b = 2(1 + 100)^3)
○ (b = 2(100)(100)(100))

Explanation:

Step1: Identify the growth - type formula

The population of bacteria has an exponential - growth model. The general formula for exponential growth is $B = B_0(r)^t$, where $B_0$ is the initial population, $r$ is the growth factor, and $t$ is the time.

Step2: Determine the values of $B_0$, $r$, and $t$

The initial population $B_0 = 100$. The population doubles every hour, so the growth factor $r = 2$. The time $t=3$ hours.

Step3: Substitute the values into the formula

Substituting $B_0 = 100$, $r = 2$, and $t = 3$ into the formula $B = B_0(r)^t$, we get $B=100(2)^3$.

Answer:

A. $B = 100(2)^3$