PLZ HELP, WILL MARK BRAINLEST
1 answer:
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Answer:
$ 12,222,222.22
Step-by-step explanation:
Let P be the initial amount distributed,
Since, the spending in first instance = 55% of P
= 0.55(P)
In second instance = 55% of (0.55(P)) = 0.55² P
In third instance = 55% of (0.55² P) = 0.55³ P,
............................., so on.....
Thus, total increase in spending = 0.55P + 0.55² P + 0.55³P.....
We know that,
0.55P, 0.55²P, 0.55³P,..............
Is a GP with infinite number of terms,
Having first term, a = 0.55P,
Common ratio, r = 0.55,
Hence, the sum of the above series,
Here, P = $ 10000000,
Therefore, total amount increase =
= $ 12,222,222.22
Answer:
Population of mosquitoes in the area at any time t is:
Step-by-step explanation:
assume population at any time t = P(t)
population increases at a rate proportional to the current population:
⇒dP/dt ∝ P
----(1)
where k is constant rate at which population is doubled
solving (1)
---- (2)
initial population = 400,000
population is doubled every week
⇒P(1)=2P(0)
Using (2)
In presence of predators amount is decreased by 50,000 per day
Then amount decreased per week = 350,000
In this case (1) becomes
---(3)
solving (3) by calculating integrating factor
Multiplying I.F with all terms of (3)
Integrating w.r.to t
at t=0
So, population of mosquitoes in the area at any time t is