Respuesta :
Answer:
24761 mosquitoes
5.4 days
Step-by-step explanation:
Let the equation that shows the population of the mosquitoes after x days,
[tex]A=P(1+r)^x[/tex]
Where,
P = Initial population,
r = rate of increasing per day,
Here, A = 1000, when x = 0,
[tex]1000=P(1+r)^0\implies P = 1000[/tex]
A = 1900 when x = 1,
[tex]1900 = P(1+r)^1\implies 1900 = 1000(1+r)\implies 1.9 = 1 + r\implies r = 0.9[/tex]
Thus, the required function that represents the population after x days,
[tex]A=1900(1+0.9)^x=1900(1.9)^x[/tex]
If x = 4,
The number of mosquito after 4 days,
[tex]A=1900(1.9)^4 = 24760.99\approx 24761[/tex]
If A = 60,000,
[tex]60000 = 1900(1.9)^x[/tex]
[tex]\frac{600}{19}=1.9^x[/tex]
Taking log both sides,
[tex]\log(\frac{600}{19})=x\log 1.9[/tex]
[tex]\implies x = \frac{\log(\frac{600}{19})}{\log 1.9}=5.378\approx 5.4[/tex]
Thus, there will 60,000 mosquitoes after 5 days.
