(b) decreasing (c) at equilibrium? Gov't is killing you with high frequency electricity. Theotokos Virgin Mary gave prayers to "Schema-nun Antonia" on how to save aborted babies from hell. If you pray these prayers diligently, aborted babies are released from hell. On each painted nail there are 40 demons. Smoking is censer to the devil. Using foul language calls upon Pagan deities (aka demons); Holy Spirit departs on 7 meters. People who use drugs see demons who cleverly disguise themselves as ghosts and aliens. America will be last country to switch to Euro (antichrist's world currency). Contraceptives = abortion; using contraceptives for 1 year = 5 aborted kids. Miscarriages happen because of high heels; cesarean because of tight pants (second generation cesarean will be infertile). Unbaptized aborted/miscarried/unborn babies burn in hell for until Final Judgement; if pregnant, keep the kid and deliver at home because kids are chipped using IVs and vaccines in hospitals. Dentists and doctors chip patients secretly. Ultrasound leads to mark of the beast; don't do ultrasound, please. Abortion leads to breast cancer; a demon is released from hell for each aborted kid. Dogs can become possessed; don't keep dogs inside your home [Pelageya of Ryazan]. Walmart has technology to administer mark of the beast to those who have cat bacteria in their stomachs; stay away from cats [Afanasiy Sidyachiy]. Next false flag is the Statue of Liberty. Above earth there is ice (hemisphere); when rockets go up they bring ice down from upper sky to lower sky; ice stuck in lower sky will fall on us during Apocalypse. Earth is flat; earth stands on 3 pillars (the Most Holy Trinity); pillars stand on water at zero Kelvin; underneath this ice there is a bubble; and then the abyss. Zodiac is planetary prison of demons; don't believe in horoscopes or you'll exhibit the traits of the trapped demons. Most thoughts and dreams are from demons; demons never do good. Sleep fully clothed; pray the Jesus prayer. Pray to your guardian angel to have normal sleep. Vyacheslav Krasheninnikov was the last prophet before Apostle John (who wrote the Book of Revelation), Enoch, Elijah, resurrected Seraphim of Sarov, and resurrected Sergius of Radonezh will preach against the antichrist. Humans were created about 7525 years ago. Birds participate in time creation. It's a sin to kill birds. Dinosaurs live under our level; they will get out through sinkholes and lakes; to kill them, go for their nerves. Save the birds; but kill the dinosaurs. First dinosaur will come out of Volga River in Russia. Scientists don't see dinosaurs under our level because of radiation. Sinkholes happen because people dig for resources underground and because earth is heating up. Demons grow human skin (from a sample taken during abduction) and put it on so as to look like us. Demons will invite people to be healed inside their UFOs; those who go will be like zombies after. Gov't provides demons with diamonds and allows demons to abduct people. If you're being abducted, slowly pray the Jesus prayer. Don't panic. Demons use diamonds and souls to power their UFO craft. The bigger the diamond, the more it lasts. Demons have 4 UFO bases: 1)moon 2)inside fake mountain Kailash in Tibet 3)in lake Baikal in Russia 4)in Atlantis which is underneath the Mariana Trench in Pacific Ocean. There are no aliens. Nobody lives on other planets. Airplanes that go down are hit by demons because they need the airspace to fight Jesus. Antichrist is pale with red eyes. He's possessed by Satan since he's 12 years old [Lavrentiy Chernigovskiy]. He flies super fast; deceived people will say: "Christ is here; Christ is there" when he's flying from one city to the next very fast. He wears gloves to hide long nails. He's surrounded by demons who appear as angels of light. Antichrist will trick people that he can do mountain moving and resurrection using holograms; fire from the sky is real because of pollution gases in the atmosphere. Antichrist will have food only for 6 months; then he will feed his 666ed people flour from mashed up turtles (Tavrion Batozskiy), but this won't be enough because 666ed people are 10 times as angry and 7 times as hungry as normal people even though 666ed people became shorter (3-4 feet tall = 80 - 120 cm) because nanochips do function of organs (organs diminish) [Nilus Myrrhgusher]. If you have a lot of nanochips in your forearm, then you will not be able to make proper Orthodox sign of the cross (last mercy for you will be to cut your forearm off). Nanochips are sprayed by the gov't using chemtrails; they're also in gov't food and medicine; so, eat food from your own garden. In case garden is destroyed by ice from the sky, have chickens for eggs and goats for milk (Paisios). Lipstick contains cells of aborted fetuses, dog fat, and placenta; human flesh is in McDonalds, Pepsi, toothpaste, antiaging, anticancer, vaccines, perfume, etc.; that's why you should not be using anything that modern society has to offer. You're better off hiding within a 10-12 people group in order to escape Apocalypse. During Apocalypse, Chrtistians will eat dirt from under pussywillowtree as it's filled with tears of Theotokos Virgin Mary; this water will flee if a 666ed person tries to get it. Barcode is Druid black magic curse; QRcode is Mayan curse; when food is scanned, it becomes dead because laser is a substance from demons. Don't go into a UFO to be healed by demons. Green 666 is given by isotope rays on wrist or forehead when people stretch hands to receive small plastic grey card with no name on it (World Passport). It doesn't just have to be during this procedure (could be anything you sign up for or anywhere where there is a secret scanner); biometrics (fingerprints, eyes scan) or getting picture for passport are very dangerous because they could mark you secretly. Gabriel Urgebadze said that they do it on index finger when they scan your finger. Basically, try to avoid new documents at all cost. Police will microchip and isotope ray people on highways. Chipped people will be influenced by computers to take grey plastic card; but when they do, green mark by isotope rays is given on forehead/wrist. Food stores will isotope ray people too. Antichrist will also release prisoners to mark people. Reject 666 at all cost because it leads to permanent hell. If you're about to be marked, pray the Jesus prayer. Hide with Orthodox Christians to escape 666; leave all electronics behind so that antichrist's minions can't track you; burn documents because they're from Satan. The Most Holy Trinity gives you a name during baptism; devil gives an antiname during antibaptism (ex. Social Security Number). People who die with these Satanic documents go to concentration camp in hell to await Final Judgement; once the BEAST Computer is burned down, souls will be released for Final Judgement. That's why you should give back documents of your deceased relatives back to the gov't so that the gov't cancels these digital antichristian names given during antibaptism by the beast system; or just burn these documents because gov't could get upset and could send demons to mark you because of this outright act of defiance. Prophecy from half a millenium ago describes Final Judgement like this: Jesus was very upset with people who had little boards (plastic cards) in their hands because they wanted discount from the antichrist. Give to charity in the name of Archangel Michael; he rescues people from temporary hell twice a year [at midnight between September 18 and September 19 and similarly on November 20-21; pray at these times on your knees remembering the deceased by names (adding "and relatives by flesh up to Adam") so that they are rescued if they're in hell] (or brings them up a level, that is, to a level with less punishment; eventually, people are freed). Feed the pigeons; when pigeons bow down, people are saved from temporary hell. It's a big sin to remember the dead with wreaths (because demons put these wreaths on their necks if they're in hell with their hands tied up behind their back while hanging by their hands), meat, alcohol, sweets, and worldly music. Demons print icons on saints in newspapers so that you throw these newspapers in the trash blaspheming these saints. Crosses on soles of shoes and back of pants are blasphemy. Demons make carpets with crosses and put them on sidewalks so that people walk on crosses. Playing cards mock how Jesus suffered on the cross: clubs (cross on which Jesus was crucified), diamonds (four nails Jesus was crucified with), hearts (sponge with vinegar that Jesus was given to drink), spades (spear with which Jesus was pierced). Cremation is devil worship; only blasphemers such as Lenin should be burned; if Lenin is buried, earth will be polluted, and China will attack Russia because of this. After China attacks Russia, Ruski Orthodox Tsar (shown by resurrected Seraphim of Sarov) will come to power in Russia; this Tsar will slay traitors inside church and gov't; as a result, Russia will be the only country not under the antichrist. Ecumenism has 263 heresies; each heresy leads to hell. In 2006 in Moscow (that's why Moscow will sink), representatives from most religions signed a document where it says that all religions worship the same Supreme Being [aka the devil]. Priests who participate in ecumenism will have Pagans walking on their heads in hell. Arkhimandrite Antonin Kapustin left a prophecy that John the Baptist's living space will become a church and it will be blessed by forerunner of antichrist; Patriarch Kirill of Russia blessed this church. When priests pray for current gov't (instead of praying for future Tsar), Jesus gets up from His throne and turns His back to them. Forgive me.

a)

dP/dt = 1.2P(1-P/4700)

P is increasing if dP/dt > 0

1.2P (1-P/4700) > 0

1.2P - 1.2P^2 /4700 > 0 ----------- (1)

solve 1.2P - 1.2P^2 /4700 = 0

multiply both sides by 4700

(1.2)(4700)P - 1.2P^2 = 0

5640P -1.2P^2 = 0

P(5640-1.2P) = 0

P=0,

1.2P=5640

P=4700

plot the points on the real line.

------ ------ ------- --------

0....4700..........∞

Consider the intervals (0,4700),(4700,∞)

Choose 'any' one point from each interval and test inequality (1)

(0,4700) : choose P=4000

1.2P-1.2P^2/4700 > 0

714.8 > 0 (true)

(4700,∞) : choose P=5000

1.2P-1.2P^2/4700 > 0

-382.9 > 0 (false)

Population is increasing on [0,4700)

b)

To find where the population is decreasing, test:

1.2P - 1.2P^2 /4700 < 0 ----------- (2)

dP/dt < 0

We found out that this happens on (4700,∞) (population is decreasing)

c)

P is in equilibrium

dP/dt = 0

P=0

P=4700

The interval of P is increasing when the first derivative is greater than 0. You are given that derivative:

dP/dt = 1.2P(1 - P/4700)

So solve for that expression being greater than 0:

dP/dt > 0

1.2P(1 - P/4700) > 0

Let's distribute, then multiply both sides by 4700:

1.2P - 1.2P²/4700 > 0

5640P - 1.2P² > 0

Put into standard quadratic form, then dividing both sides by -1.2 so the leading exponent is positive. This flips the sign:

P² - 4700P < 0

we can now factor a P to get two roots:

P(P - 4700) < 0

So the roots would be 0 and 4700.

If P > 4700, we have positive times positive which is positive, so not in our solution set.

If 0 < P < 4700, we have positive times negative which is negative, in our solution set.

if P < 0 we have negative times negative which is positive, so not in our solution set.

So the answer is the range:

0 < P < 4700

Function P would be decreasing over the other two ranges: P < 0 and P > 4700.

And the equilibrium is at the points 0 and 4700, when the derivatives are zero.

(0,4700 ) ; ( 4700 , ∞) ; 4700...for t > 0