there is a population of 56,950 bacteria in a colony. if the number of bacteria doubles every 370 hours…

there is a population of 56,950 bacteria in a colony. if the number of bacteria doubles every 370 hours, what will the population be 1,850 hours from now? bacteria

there is a population of 56,950 bacteria in a colony. if the number of bacteria doubles every 370 hours, what will the population be 1,850 hours from now? bacteria

Answer

Explanation:

Step1: Calculate doubling - times

First, find out how many times the bacteria doubles. Divide the total time elapsed by the time for one - doubling. Let $n$ be the number of doubling - times. $n=\frac{1850}{370}=5$.

Step2: Calculate final population

The initial population $P_0 = 56950$. The population after $n$ doublings is given by the formula $P = P_0\times2^n$. Substitute $P_0 = 56950$ and $n = 5$ into the formula: $P=56950\times2^5$. $2^5=32$, so $P = 56950\times32=1822400$.

Answer:

1822400