a. Find the rate of change of the growth rate with respect to the amount of food.   b. The quantity A in the formula for f ( x ) represents the quantity of food for which the growth rate is half of its maximum. Using the answer from part a, find the rate of change of

Q: The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by…

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: The growth model for a population of bacteria is given as P(t) = 50e2t where t is measured in days.…

A: Given: The growth model is  P(t) = 50e2t where t is measured in days. When P(t)= 25,000  find t

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: (b)

Q: Find the time required for an initial investment of $2000 to reach $3500 if the interest is…

A: Topic- continuous compound interest

Q: Find the average rate of change of g (x)=x-4x+1 from x 2 to x 6. Simplify your answer as much as…

A: Given data: The given function is g(x)=x2-4x+1. The lower limit of x is a=2. The upper limit of x is…

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

A: This question is related to the population growth, We will solve it using integration.

Q: An investment of $75,000 increases at a rate of 12.5% per year. Find e value of the investment after…

A: An investment of 75,000 increases at a rate 12.5% per year. Find the value of the investment after…

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: As an analyst at Decimating Capital, you are asked to estimate the future revenue of the Slate Rock…

A: The revenue function modeled by the equation Rt=0.825t0.04 Here Rt=drtdt Where r(t) is revenue…

Q: Suppose the formula B = 5√T yields a good approximation to the amount of bacteria, as measured by…

A: To find the instantaneous rate of change of B with respect to T, differentiate B=5T with respect,…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Given expression is PV1.4=C   ......1 Where P is pressure, V is volume and C is constant.  Pressure…

Q: The gross domestic product (GDP) of a certain country is projected to  be N(t) = t2 + 2t + 50 ( 0 ≤…

A:

Q: f) The population of a town grows at the rate of 3% per year (compounded continuously). How long…

A:

Q: If x is measured in months where x=0 represents January of 2000, and F(x) represents the US GDP…

A: given GDP is measured in  millions of dollars  x is measured in months

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given data÷ Cost function is given by C(x)=0.2x2+7000 Where,x=unit produced per month We have to…

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

A: We use differentiation and integrations to solve this problem.

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given: A potato initially has a temperature of 75 degrees and the oven is preheated to 375 degrees.…

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: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given that, the cost to produce x units per month is given by                C = 0.3x2+8,000  and…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given query is to find the rate of change of cost.

Q: 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in…

A: The growth rate of a colony of ants is given by 10t/(1+t2)2 Initially there are 100 ants ∴ Number of…

Q: 10 If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does S g'(x)dx…

A: Given, g'(x) is the rate of growth of redwood tree in feet per year now, We have to define…

Q: THe model for the growth rate of tumor known as the Gompertz Tumor Growth is given by the following…

A:

Q: 1. The value of the car, x years after it is purchased, is given by the following equation: 27000…

A:

Q: Park service personnel are trying to increase the size of the bison population of a large park. If…

A:

Q: Answer the following as detailed as possible. 1. If the growth rate of a culture of bacteria is…

A: Let P is initial population of Bacterial, A is present population of bacteria in time t, We know…

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: The value of a computer t years after purchase is V(t) = 2, 000e-0.35t dollars. At what rate is the…

A:

Q: A culture initially has No number of bacteria. At t =1hours the number of bacteria is measured to be…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 2000 cells…

A: Here, the initial population given is 2000, and its doubles after 2 hours.

Q: Park service personnel are trying to increase the size of the bison population of a large park. If…

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A:

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: If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does (see picture)…

A: solution is given below

Q: A new computer costs $2000 today and decreases in value at a constant rate of $500 per year. Denote…

A:

Q: Suppose Shunreca Garner invested $8000 in stocks and the investment grew exponentially to $10000 in…

A: To use the exponential model to 1) determine the  growth rate and 2) to calculate the value after 15…

Q: 7. If the rate of growth of a bacteria population is modeled by r(t) = 8e2t-1 thousand bacteria per…

A: Introduction: When a function is given, we determine the average value by integrating the function.…

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: The following equation represents the growth of bacteria in a particular food product, where t…

A: Given, the number of bacteria function f(t) = 700e0.1t , where t is time in days. When the bacteria…

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the volt-age…

A: Separate the variables.

Q: ズ-1 f(x) = X + 3

A: given: f(x)=(x-1)/(x+3) x=4 delta(x)=8

Q: National Park Service personnel are trying to increase the size of the bison population of the…

A: The increase in population can be calculated as shown below.

Q: The rate of growth of a fish population was modeled by the equation G(t) =…

A: Consider the given: Gt=90000e−0.6t1+5e−0.6t2

Q: Suppose you have a clothes dryer that uses 4000 watts of power and run it for an average year f 1…

A: To determine the operational cost of the hair dryer.

Q: If a population grows exponentially at a rate r, the time it will take for the population to double…

A: We can derive the formula for the time it will take for the population to double using the basic…

Q: A tumor is approximately modeled by the shape of a sphere, given by the following equation: 3 V = =…

A: Through a series of suggested steps, we have to calculate the rate of change of volume, dV/dt

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.