Question

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 exponential - growth formula

The general formula for exponential growth is $B = B_0(r)^t$, where $B_0$ is the initial amount, $r$ is the growth factor, and $t$ is the time.

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

The initial number of bacteria $B_0 = 100$, the growth factor $r = 2$ (since the population doubles), and the time $t = 3$ hours.

Step3: Substitute the values into the formula

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

Answer:

$B = 100(2)^3$