A company has found that its rate of expenditure​ (in hundreds of​ dollars) on a certain type of job is given by E′(x)=4x+5, where x is the number of days since the start of the job. Find the total expenditure if the job take 2 days.

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: Given the rate of change of a quantity Q and its initial value Q(0), explain how to find the value…

A: Given: the rate of change of a quantity Q and its initial value Q(0), To find: the value of Q at a…

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

Q: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

A: Given that the growth function is: y(t) = y0ekt. At, t=0, y(0) = y0 [This is the initial…

Q: A radioactive material is known to decay at the rate proportional to the amount present. If…

A: Given A radioactive material is known to decay at the rate proportional to the amount present.…

Q: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

Q: part ii, thank you very much.

A:

Q: After the introduction of foxes on an island, the number of rabbits on the island decreases by 4.5%…

A:

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Solve for the value

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: As population is proportional to present population. So we need to form a differential equation. and…

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: To find the rate of change of the carbon monoxide levels per population when t=2

Q: In a particularly small region in the Philippines, the consumer price index C depends on • E, the…

A: Given that, The consumer price index C, which depend on The current value of the gross Domestic…

Q: 5. If the population P of bacteria (in units of 1000) is declining because of a toxin, its rate of…

A:

Q: A population of mites growsat a rate proportional to the number present, y. If the growthconstant is…

A: Assume population at time t is p Let f(t)=population at time t=p

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: e) What are the domain and the range for this situation?

A:

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: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given that: Rate of increase of population is proportional to the number of people in the country.At…

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x+3x at x= - 1 The…

A:

Q: A bacteria colony grows at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: We are given that the grow after each year is 11%, that means if the initial value is x, then the…

Q: The population of a colony of bacteria is modeled by the function P(x) = 50(e-X -e-X* ) + 10, for 0…

A: Given that: P(x)=50(e-x-e-x2)+10

Q: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: Suppose a tank contains 8000 gallons of oil, and this is being pumped out at a rate of 600e ,-0.05t…

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A:

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: Based on the data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

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

A:

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: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A:

Q: A certain radioactive substance is decaying so that at time t, measured in years, the amount of the…

A:

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

A: Exponential growth/decay is given by dxdy=rici-r0vx here, ri=3= rate of drug entering. and r0=3=…

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60) where x…

A: Given that the monthly output is Qx=15,000+2x2 units, where x is the number of workers. Find Q'52.

Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

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: find the function that gives the value of the investment as a function of t. (Round your value of k…

A:

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

A:

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

A:

Q: Rank the functions x100, ln x10, xx, and 10x in order of increasinggrowth rates as x→ ∞.

A:

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

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: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

A:

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

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.