Question

(b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day, what is thesize of the colony after 3 days?Approximately mosquitoes(Do not round until the final answer. Then round to the nearest whole number as needed.)}.vix

Answer 1

Given:

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day,

Required:

what is the size of the colony after 3 days?

Explanation:

We know

$A=A_0e^{kt}$$\begin{gathered} Where, \\ A_0=\text{ Starting amount} \\ e=\text{ Euler's constant} \\ k=\text{ Amount of increase} \\ t=\text{ time} \end{gathered}$

Now,

$\begin{gathered} 1500=1000e^k \\ \frac{1500}{1000}=e^k \\ 1.5=e^k \\ ln1.5=klne \\ k=0.405 \end{gathered}$

After 3 days

$\begin{gathered} A=1000\times e^{(0.405\times3)} \\ A=1000\times e^{1.215} \\ A=1000\times3.370 \\ A=3370 \end{gathered}$

Answer:

After 3 days there will be 3370 mosquitoes.