3. A rocket weighs 2000 tons at liftoff and burns fuel at a rate of 10 tons/minute. Express the rocket's weight W(in tons) as a function of the time t (in minutes) after liftoff.

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: Estimate the instantaneous rate of change at x= 1 for Ax) = /x + 1. a) -2 b) -0.5 c) 0.5 d) 2

A:

Q: The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is…

A: To find the maximum value, P''(I)<0. If this condition satisfies, then P will be maximum at I.

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A:

Q: Estimate the instantaneous rate of change of the function at x = -2. 2 (2, 0) -4 4 -2 -4 (-3, –5) a)…

A: Given:

Q: 5. Find the instantaneous rate of change of 1 g(x) = 2x – 32x° + 17x² – 9x + 4 at x = 2

A: Given equation is, gx=2x4-32x3+17x2-9x+4

Q: A population of bacteria is initially 8000. After three hours the population is 4000. If this rate…

A: Given,          A population of bacteria is initially 8000. afters three hours the population is…

Q: 2. In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution is given below:

Q: 4) How quickly is an airplane's elevation currently rising if its height (in feet) as a function of…

A: We need to find rate of change of elevation or rate of change of height when t = 4 sec Hence we will…

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: If the population (in millions) of a country as a function of time (in years) is P(t) = 10 · 2kt,…

A:

Q: f. Assume that the population of a certain city increases at a rate proportional to the number of…

A: Note: Since the image contains multiple questions, as per the answering guidelines we are to solve…

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: 9. The rate at which the value, V, of a painting changest years after it is completed is given by…

A: Image is attached.

Q: A particular radioactive isotope has a half-life of 400 years. The time required for only A% of the…

A: The half-life of the radioactive element is the time during which half of the radioactive element…

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: The rate (in mg carbon/m°/h) at which photosynthesis takes place for a species of phytoplankton is…

A:

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: Given that a company can produce 12,000 units when the number of hours of skilled labor y and…

Q: 7. Determine the rate of change for a function that h y 27 12 2 22 -1 7 1 17

A:

Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

A:

Q: A population of bacteria can be modeled by the function f(t)=1000(0.98)t where t represents the time…

A:

Q: A colony of fruit flies grows at a rate proportional to its size. At time t = 0, approximately 20…

A: Let the population of fruit flies be modelled by function y.  The question mentions that the rate is…

Q: Use Definition 1 or 2 to find the instantaneous rate of change of the function at the given value…

A:

Q: pressure

A:

Q: Between 2006 and 2016, the nurmber of applications for patents, N, grew by about 3.6% per year. That…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

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A:

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

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A: The approximating function that represents the given scenario is: g(x)=53.1+63.1 ln(x) where x…

Q: Suppose that y = C(t) represents the average cost of a gallon of milk in the United States t years…

A: represents the change in the average cost of a gallon of milk in the United States t years since…

Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

A:

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: determine the instantaneous rate of change for the function f(x)=7^x + 9log(x^x) at x=4

A: This question can be solved using the concept of derivative of a function at a point.

Q: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

A: To determine the counting function P(t) explicitly, under the given conditions

Q: #3 Find the instantaneous rate of change for the function f(x) = V3 – x at x = -6.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: 9. Determine the average rate of change for the function, f(x) = -4.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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: 1. A truck that delivers essentials in remote areas can travel 85 kilometers. Which of the following…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: We can use a linear function to describe air leaking from a balloon, but this is not, in fact, an…

A:

Q: What is the average rate of change of f(x)=log2x from 8 to 32. what is the equation of the seant…

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Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

Q: 3) An empty can of room freshener that has a volume of 350 mL, contains gas at a pressure of 360 kPa…

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

Q: 13. Snow falls during a storm at a rate of t(4–t) inches per hour, as a function of time t in hours.…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A:

Q: estimate the instantaneous rate of change at the point indicated. P(x) = 3x^2 − 5; x = 2

A: To find the  the instantaneous rate of change at x=2 we need P'(2) We first find P'(x) using the…

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A: