![cristabean87](/avatars/16997.jpg)
cristabean87
05.05.2020 •
Mathematics
If N is the population of the colony and t is the time in days, express N as a function of t. Consider Upper N 0 is the original amount at tequals0 and knot equals0 is a constant that represents the growth rate. N(t)equals eN0et e Superscript t(Type an expression using t as the variable and in terms of e.) (b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days? Approximately nothing mosquitoes. (Do not round until the final answer. Then round to the nearest whole number as needed.) (c) How long is it until there are 20 comma 000 mosquitoes? About nothing days.
Solved
Show answers
More tips
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Society and Politics Is It Fact or Fiction? Let s Talk About Anton Chekhov s Pseudonym...
- S Sport Playing Bowling: Rules and Advice for Novices...
- C Computers and Internet How to Properly Repartition a Hard Drive?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
- C Computers and Internet Which Phone is Best for Internet Surfing?...
Answers on questions: Mathematics
- M Mathematics Brainlist . answer with an actual good answer or i will report...
- M Mathematics Find the equation of the tangent to the parabola. 1.at (3/2 , 6)2.at (6,3)...
- M Mathematics i still need help finding angle 1 and 2...
- M Mathematics Please look the picture...
- M Mathematics Help me please I will mark BRAINLIEST...
- M Mathematics Solve the function :f(x) = [-3.41]...
- M Mathematics Complete the table and graph the function....
- M Mathematics A In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 4.0 inches. A study participant...
- M Mathematics If the cost of 1 kg of rice is RS 85 whole 1/2 ,find the cost of 10 kg of rice with formula...
- M Mathematics Helpppppppppppppppppppp...
Ответ:
(a)![N(t)=Noe^{kt}](/tpl/images/0640/3576/86c39.png)
(b)5,832 Mosquitoes
(c)5 days
Step-by-step explanation:
(a)Given an original amount
at t=0. The population of the colony with a growth rate
, where k is a constant is given as:
(b)If
and the population after 1 day, N(1)=1800
Then, from our model:
N(1)=1800
Therefore, our model is:
In 3 days time
The population of mosquitoes in 3 days time will be approximately 5832.
(c)If the population N(t)=20,000,we want to determine how many days it takes to attain that value.
From our model
In approximately 5 days, the population of mosquitoes will be 20,000.
Ответ:
a) N(t) = Noe^kt
b) 5832mosquitoes
c) Approximately 5years
Step-by-step explanation:
If he rate of growth is equal the number of population present in a given time, we have:
dN/dt ∝ N
N is the number of population.
dN/dt = kN
k is the constant of proportionality
dN = kNdt
On separating the variables
dN/N = kdt
Integrating both sides of the equation, we have
∫dN/N = k∫dt
ln(N/No) = kt
Taking exp of both sides
e^ln(N/No) = e^kt
N/No = e^kt
N = Noe^kt
N(t) = Noe^kt
No is the original amount of population
t is the time in days
b) If there are 1000 mosquitoes initially and there are 1800 after 1 day,
N = 1800, No = 1000 at t = 1
1800 = 1000e^k(1)
1800/1000 = e^k
e^k = 1.8
Taking ln of both sides
lne^k = ln1.8
k = ln 1.8
k = 0.5878
To get the size of the colony after 3 days,
N(t) = 1000e^0.5878(3)
N(3) = 1000e^1.7634
N(3) = 1000×5.832
N(3) = 5832
The size if the colony after 3years is 5,832mosquitoes
c) To determine how long is it until there are 20,000 mosquitoes?
N(t) = Noe^kt
20,000 = 1000e^(0.5878)t
20,000/1,000 = e^0.5878t
20 = e^0.59t
ln20 = lne^0.5878t
ln 20 = 0.5878t
t = ln20/0.5878
t = 5.07years
It will take 5years until there are 20,000mosquitoes
Ответ:
x-1 multiple 2x-1 = f(-x)