The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1900 after 1 day, what is the size of the colony after 4 days? How long is it until there are 60,000 mosquitoes? What is the size of the colony after 4 days? mosquitoes (Round to the nearest whole number.) How long is it until 60,000 mosquitoes are in the colony? days (Round to the nearest tenth.)

Answer:24761 mosquitoes5.4 daysStep-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.