Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A wea balloon is filled with hydrogen at the rate of 0.5 ft/s. Initially, the balloon has 3 ft of hydrogen. (a) Find a linear function V that models the volume of hydrogen in the balloon at any time t. V(t) = (b) If the balloon has a capacity of 17 ft, how long does it take to completely fill the balloon?

Q: 3. A rocket weighs 2000 tons at liftoff and burns fuel at a rate of 10 tons/minute. Express the…

A: Given query is to find function of the weight after t time of the 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: 22. If f(0)= 20, and f(1)=25, find a linear model and an exponential model for f(x).

A: “Since you have asked multiple Questions, we will solve the first question for you. If you want any…

Q: A large koi pond is filled from a garden hose at the rate of 10 gal/min. Initially, the pond…

A: a) Given that initially, there was 300 gal of water.  And water is entering at a rate of 10 gal/min.…

Q: Let f(x) = (x + 5)² and g(x) = 1 – 5x. (a) Only one of the two functions f and g is linear. Which…

A:

Q: The rate of increase of the population of a certain city is proportional to the population. In 1970,…

A:

Q: A 2005 study by the Fisheries Research Services in Aberdeen, Scotland, suggests that the average…

A:

Q: Avalanche forecasters measure the temperature gradientdT/dh, which is the rate at which the…

A: Given that Avalanche forecasters measure the temperature gradient dT/dh. He uses the following rule:…

Q: In 1995, the rate of violent crimes in New York City continued to decrease, but at a slower rate…

A:

Q: For positive constants c and k, the Monod growth curve describes the growth of a population, P, as a…

A: Given: P=crk+r Recall: uv=u'v-v'uv2

Q: 12. f(x)=5-2/5x  express it in the form f(x) =ax+b and state the rate of change of the function.

A: Given:  fx=5-25x To Find:  To express the given function into the form, fx=ax+b, and to state the…

Q: The decrease in the number of colonies of honey bees, essential to pollinate crops providing one…

A:

Q: The rate of natural increase of the population of a certain city is proportional to the population.…

A:

Q: When the price of a book is $125, a book store can expect to sell 600 books. If the price rises to…

A:

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

A:

Q: The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain…

A: As per bartleby policy I answered the first two subparts

Q: A small brewery considers the output of its bottling machine as a continuous income stream with an…

A: Given that the output of its bottling machine as a continuous income stream with an annual rate of…

Q: A highway patrol plane flies 3 mi above a level, straight road at a steady 120 mi/h. The pilot sees…

A: Given:

Q: As a fungus grows, its rate of growth changes. Young fungi grow exponentially, while in larger fungi…

A:

Q: A population of fish is modeled by the equation dP/dt = .00016P(1300-P)+20 with an initial…

A: Roots of quadratic equation Plotting of graph of Quadratic equation with the help of roots. Basic…

Q: The population of a city grows from an initial size of 100,000 to an amount P given by P(t) =…

A:

Q: Gonorhea is spread by sexual contact, takes 3 to 7 days to incubate, and can be treated with…

A:

Q: 5. Find the instantaneous rate of change of the value function V in terms of t and N(t).

A: To find the instantaneous rate of change of the value function V in terms of N we will find dVdN…

Q: A hot air balloon launches straight up into the air from the top of a hill with an elevation of 200…

A: Given time=t, elevation = E Given that at t=0 minute, h=200 feet At t=20 minute, h=620 feet So two…

Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: We have to find rate of climb of airplane at t=180 sec.

Q: If q'(t) is the growth rate of a population of a fish population in fish per month, what does…

A:

Q: A cylindrical tank holds 20,000 gallons of water, which can be drained from the bottom of the tank…

A:

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A: Use the formulas below to evaluate dP and ∆P . dP=P'(x)dx∆P=P(x2)-P(x1) Here, dP is the approximate…

Q: considering that the rate of decay is proportional to the cube of the material

A: When a proportionality sign is removed the constant is applied with the equal sign.

Q: A large koi pond is filled from a garden hose at the rate of 15 gal/min. Initially, the pond…

A: Given: rate with which garden hose can fill the pond=15 gal/ min  initially in the pond the content…

Q: As a fungus grows, its rate of growth changes. Young fungi grow exponentially, while in larger fungi…

A: The given problem is solved below in detail.

Q: A large koi pond is filled from a garden hose at the rate of 19 gal/min. Initially, the pond…

A:

Q: 27. The linear function f has rate of change 3 and initial value –1

A: (27). Rate of change of the function, f'(x) = 3 Initial value of the function, f(0) = -1

Q: Find the maximum rate of change of f(s,t)= te^{st} at the point (0,5).

A: In this question we have to find the maximum rate of change.

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

A:

Q: in a single-species forest. T2 30- 25- 20- 10 y-f(t) 15+ 10+ 10 12 20 30 40 50 Years Here f(t) is…

A: Solution The following slopes are calculated with the help of given graph. The slope of tangent,  is…

Q: S. Show that the two functions y = Aet (interest compounding) and y2 = Aert (discounting) are mirror…

A:

Q: The graph of a linear function f is given. (a) Find the rate of change of f. (b) Express f in the…

A: If we have a function f(x)and function passes through two points (a1, b1) and (a2, b2) , then rate…

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: The number of bacteria in a culture is given by the function n(t)=950e^0.35t where t is measured…

A: The number of bacteria in a culture is given by n(t) = 950e^{0.45t}e0.45t

Q: After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood…

A: Consider the given function  Ct=0.135 t·e-2.802 t

Q: The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption…

A: average blood alcohol concentration is given byC(t)=0.00225te-0.0467twhere t is in minutes and C is…

Q: A large koi pond is filled from a garden hose at the rate of 18 gal/min. Initially, the pond…

A: It is given that the garden hose is filling with water at a rate of 18 gal/min. The initial volume…

Q: Let f(x) = (x + 5)² and g(x) = 1 - 5x. %3D (a) Only one of the two functions f and g is linear.…

A: Here we have,  f(x)=(x+5)2 and g(x)=1-5x

Q: After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood…

A: Here, the given function is: C(t)=0.135te-2.802t...(1) which models the average BAC, measured in…

Q: 2. In a community of 10000 people, the rate at which a rumor spreads is jointly proportional to the…

A: Let ‘n’ be the number of people who have heard the rumor 10000-n be the number of people who have…

Q: A certain gas satisfies the equation PV1.4 = C, where C is a constant, P is the pressure, and V is…

A: Given equation : P = 20 kg/cm2   V = 32  cm3dVdt=-2 cm3/min

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.