At the start of 2010, an online social group had 360 million members. Subsequently, new members joined at a rate of roughly m(t) = −6.6t2 + 16t + 250 million members per year    (0 ≤ t ≤ 5), where t is time in years since the start of 2010. (a) Find an expression for the total online social group membership M(t) at time t. HINT [See Example 6.] M(t) =     (b) Use the answer to part (a) to estimate the online social group membership midway through 2013. (Round your answer to the nearest 1 million members.) M(3.5) = million members

Q: Over 4 years, researchers studied the growth of a fish population and found its growth rate to P'(t)…

A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

Q: A tank originally contains 100gal of brine solution containing 20lbs of salt. At t=0, pure water is…

A:

Q: 4. Micky starts a retirement account at age 32, putting away $250 each pay period, of which he has…

A: Given that the amount of money at time, t with a rate 4% is, ft=6000e0.04t Suppose that the…

Q: 2) y = –2 (5)* Initial Value: Constant Ratio: Asymptote:

A:

Q: ) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 25% per…

A: Given query is to find the expression for the population after t years.

Q: Suppose that the fish population P(t)in a lake is attacked by a disease at time t=0, with the result…

A: From the given data, dPdt=βt-δtPβ=0δ=kPP0=100,000P20=1984Px=0x=?

Q: The population of a community grows in proportion to the population at any time t. Its initial…

A: Given data is: Initial population P=1200 R=25% Time t=8 year

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

Q: The growth of bacteria in food products makes it necessary to time-date some products (such as milk)…

A: Given, ƒ(t) = 500e0.1t  t- in days f(t)- in millions.

Q: 2. The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: (For Bacteriologists). In one of your Basic Calculus sessions, a top of the class Grade- 12 student…

A: Hair we have to find out the value of Y for the different values of T

Q: Suppose that I years from now, one investment plan will be generating profit at the rate of P1'(t)=…

A: Given. P1'(t) = 90e0.1t (1000$) P2'(t) = 140e0.07t (1000$)

Q: The population of a community is growing at 2% per year and its per capita consumption is growing at…

A: Given that: Population growing rate of a community is 2% per year Per capita consumption growth rate…

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: It is estimated that t years from now the population of a certain lakeside community will be…

A: The population is changing at the rate of 0.6t2+0.2t+0.5 thousand people per year. That is,…

Q: When it comes to bacteria growing by binary fission, its generation time will be the time interval…

A: Given,              G=t3.3 logbB; G= generation time  t=  time interval in hours or minutes b=…

Q: World consumption of lead is running at the rate of 4.7e0or million metric tons per year, where t is…

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about…

A: Refer to the question we have to find when the Egyptian die. It is given that amount of carbon-14…

Q: The number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A: a) Revenue per user at t = 0  = $ 350  Then it decreases by 10% every year, i.e. revenue per user at…

Q: 1) The development of a new amusement park on the outskirts of a city is expected to increase the…

A: Rate of increase in population is . The projected population will be given by integrating the rate…

Q: 2. In 1998, the average annual cost of a public college was $8,850 and costs were climbing by 8% per…

A: 2. The general form of the formula is final value = initial value×1+r%t The formula we have to use…

Q: It has been estimated that the total production of oil from a certain oil well is given by T(t) =…

A:

Q: An efficiency study of the morning shift at a certain factory indicates that an average worker who…

A: Given, Qt=-t3+6t2+24t a. Compute the worker's rate of production at 11:00 A.M. Here t=3 ( Difference…

Q: The number N() of people In a community who are exposed to a particular advertisement is governed by…

A:

Q: 2. The liquid base of an ice cream has an initial temperature of 210°F before it is placed in a…

A: Given : The liquid base of an ice cream has an initial temperature of    To find at what time will…

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: Suppose that the number of bacteria in a culture at time t is given by N = 5000 (25 + te ). (a) Find…

A: Given that the bacteria culture model at a time t is given as  Nt=500025+te-t20 To find the largest…

Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

A: ∫xndx = xn+1n+1 + C, where 'C' is the constant of integration.

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: 13. The revenue from a manufacturing process (in millions of dollars) is projected to follow the…

A: R = 100 + 0.08t at t = 10 R = 100 + 0.8 R = 100.8 million dollars.   C = 60 + 0.2 t2 at t = 10 C =…

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A:

Q: A population of insects increases at a rate of 20010t 0.25t2 insects per day 3. (t in day units).…

A: It is given that initially there are 35 insects at t = 0. So, I (0) = 35.

Q: A bacterial colony is rapidly expanding. It has 10 bacteria at time t=0 and 2000 bacteria at time…

A: As per our guidelines we only solve first question and rest of the question will be reposted.

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: 1. There are 64.000 subscribers to an online fashion magazine. Due to competition from a new…

A:

Q: 9. From 1975 to 2009, the age-adjusted incidence rate of invasive lung and bronchial cancer among…

A:

Q: A tank initially contains 400 gal of fresh water. At time t=0, a brine solution witha concentration…

A: We will find amount of solution after t min and then find time required to empty the tank  To find…

Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

Q: A tank initially contains 20 L of water. A solution containing 1 g/L of chemical flows into the tank…

A: Let's find.

Q: A radioactive element decays according to the function Q= Qn e", where Q, is the amount of the…

A: Given that a radioactive element decays according to the function Q=Q0ert, where Q0is the amount of…

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Given relation is: Qt=-t3+6t2+24t a). The worker's rate of production at 11 AM: So put t=3 in given…

Q: 2) y = -2 (5)* Initial Value: Constant Ratio: Asymptote:

A:

Q: The amount of decay of a certain radioactive element is given by -0.04t Yoe' where t equals time in…

A: The amount of decay of the radioactive element is given as follows. y=y0e-0.04t where t is the time…

Q: A radioactive element decays according to the function Q = Q, et, where Q, is the amount of the…

A: Given:     Q=Q0ert   where Q0 is the amount of substance at t = 0.       r=-0.00027  Q is the amount…

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem

Q: Suppose the following graph represents the number of bacteria in a culture t hours after the start…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.