Question

question 16 of 22. a colony contains 900 mosquitoes, which doubles every 3 hours. consider the population of mosquitoes as a function of time in hours. what will be the population of the mosquitoes after 18 hours?

Explanation:

Step1: Determine number of 3 - hour intervals

The time elapsed is 18 hours. The number of 3 - hour intervals $n=\frac{18}{3}=6$.

Step2: Use exponential - growth formula

The initial population $P_0 = 90$. The population doubles every 3 hours, so the population formula is $P = P_0\times2^n$. Substitute $P_0 = 90$ and $n = 6$ into the formula: $P=90\times2^6$.

Step3: Calculate $2^6$

$2^6=2\times2\times2\times2\times2\times2 = 64$.

Step4: Calculate final population

$P=90\times64 = 5760$.

Answer:

5760