if the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150…

if the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria, what will the population be 1,152 hours from now? bacteria

if the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria, what will the population be 1,152 hours from now? bacteria

Answer

Explanation:

Step1: Calculate doubling - times

Find how many 384 - hour intervals are in 1152 hours. Let $n$ be the number of doubling - times. $n=\frac{1152}{384}=3$.

Step2: Use the population - growth formula

The initial population $P_0 = 2150$. The population formula for doubling is $P = P_0\times2^n$. Substitute $P_0 = 2150$ and $n = 3$ into the formula. $P=2150\times2^3$.

Step3: Calculate the final population

$2^3=8$, so $P = 2150\times8=17200$.

Answer:

17200