A new fast-food firm predicts that the number of franchises for its products will grow at the rate dn 9/t + 1 dt where t is the number of years, 0

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: Given An environmentalist find that a certain types of tree grows in such a way that its height h(t)…

Q: A population of insects increases at a rate of 200 + l0t + 0.25t 2 insects per day (t in days). Find…

A:

Q: as x increases uniformly at the rate of 0.0017 feet per second, at what rate is the expression (1+x)…

A:

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: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Consider the population of fish in a lake, and that people commonly fish in this lake. At a given…

A: The differential equation given is as follows:…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials…

A:

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: if two resistors with resistances R1 and R2 are connected parallel, then the total Resistance R…

A: Given,

Q: The Ideal Gas Law is PV = mRT where P is the pressure, V is the volume, m is the constant mass, R is…

A:

Q: 2. Suppose that at some time t the mass of the tumor, M(t), is between 0 and K. What is the sign of…

A: We need to find sign of rate of change of M.

Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

A:

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

A:

Q: A population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day (t in days). Find…

A: Given that, The population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day. At…

Q: Solve this differential equation using power series: y''+y=kx^2 where k is a constant.

A:

Q: the number of U.S. Citizens aged 65 year and older from 1900 through 2050 is estimated to be growing…

A: Given: Rt=0.063t2-0.48t+3.87 As it is given that 0≥t≤15 Hence, t=0 for 1900 and t=10 for 2000 and…

Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The 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: The number of customers in a store is modeled by the function P that satisfies the logistical…

A:

Q: The differential equation for a freee-falling mass m near the surface of the earth is given by:…

A: Consider the equation:

Q: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A:

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: A rock contains two radioactive isotopes, R. series; that is, RA, decays into RA2, which the at…

A:

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

A:

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: We have to determine the time necessary for the number of bacteria to triple.

Q: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: The population of two different species are given by P1 P1 = 3 ln(t) + 10 || and P2. , where t is…

A: The population of two different species are given by P1=3lnt+10 And P2=6lnt+2 Where, t measured in…

Q: Suppose that z = x³y²2, where both x and y are changing with time. At a certain instant when x = 1…

A: The product rule of differentiation states that ddtfg=fdgdt+gdfdt. The power rule of differentiation…

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

A:

Q: The number of field mice in a certain pasture is given by the function 200 – 10t, where time t is…

A: Given: The function for the number of mice in the field = 200 - 10t To find: The differential…

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Solution

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A:

Q: A deposit of $2000 at 2% interest compound continously will grow to v(t)= 2000e0.02t dollars after t…

A:

Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

A:

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: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

A:

Q: A radioactive material, such as one of the thorium isotopes, thorium-234, decays at a rate…

A: We will find the rate of decay as following.

Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

A: