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Pepsi [2]
3 years ago
9

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

re 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.)
Mathematics
1 answer:
STatiana [176]3 years ago
6 0

Answer:

24761 mosquitoes

5.4 days

Step-by-step explanation:

Let the equation that shows the population of the mosquitoes after x days,

A=P(1+r)^x

Where,

P = Initial population,

r = rate of increasing per day,

Here, A = 1000, when x = 0,

1000=P(1+r)^0\implies P = 1000

A = 1900 when x = 1,

1900 = P(1+r)^1\implies 1900 = 1000(1+r)\implies 1.9 = 1 + r\implies r = 0.9

Thus, the required function that represents the population after x days,

A=1900(1+0.9)^x=1900(1.9)^x

If x = 4,

The number of mosquito after 4 days,

A=1900(1.9)^4 = 24760.99\approx 24761

If A = 60,000,

60000 = 1900(1.9)^x

\frac{600}{19}=1.9^x

Taking log both sides,

\log(\frac{600}{19})=x\log 1.9

\implies x = \frac{\log(\frac{600}{19})}{\log 1.9}=5.378\approx 5.4

Thus, there will 60,000 mosquitoes after 5 days.

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