Help, I have no idea where to even begin

The colony size after 4 days is 10 497.

There will be at least 90 000 mosquitoes on the 8th day.

Step-by-step explanation:

The law of uninhibited growth means the mosquitoes will increase using this formula for exponential growth:

y = abˣ

"y" is the total population after "x" time

"a" is the initial population

"b" is the rate of growth or decay

Initial population  a = 1000

Rate of change

b = 1800/1000

b = 1.8                   A positive rate of change means growth

The time passed is 4 days, x = 4

Substitute the values and find "y" for the population after 4 days:

y = abˣ

y = (1000)(1.8)⁴                        Do the exponent first

y = (1000)(10.4976)                Multiply

y = 10497.6

We can't have 0.6 of a mosquito, so the population is y = 10 497.

If we want to find "x" (time) until y = 90 000, substitute the same "a" and "b" values. The rate of change and starting population are the same. Then, isolate "x".

y = abˣ

90 000 = (1000)(1.8)ˣ

90000 / 1000 = 1.8ˣ                   Divide both sides by 1000

90 = 1.8ˣ

We can find "x" by trial and error or using "log" on the calculator. I will use log.

x =

The base is 1.8, and "ans" (answer) is 90.

x =

x ≈ 7.65515....

On the seventh day, you will not have 90 000 mosquitoes yet. You have to wait until the next day.

You also can't use a decimal number because you don't know when the mosquitoes are born during day 7.

x ≈ 8                      

Therefore, it will be 8 days until there are 90 000 mosquitoes.

answer:

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