Suppose that in a memory experiment the rate of memorizing is given by M'(t)=−0.004t2+0.9t where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 15 minutes?

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A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

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Q: consider a tree with a tr

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Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

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A: Given the rate of change= 0.6+4/(t+2)2 feet per year To find the total number of feet grown during…

Q: .

A: We will find the temperature.

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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

A:

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: snip

A: Given: fx=3x-5 To Find: The average rate of change of the given function from x=0 to x=4

Q: 2. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

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

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

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

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Q: When a company sells a product with a lifetime guarantee, the number of items returned for repair…

A: This question related to integration.

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Q: A quantity with an initial value of 110 grows continuously at a rate of o.5% per hour. What is he…

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

A: The decay rate is proportional to the amount present. So, dNdt=-λN⇒dNN=-λdt⇒∫dNN=-λ∫dt+C⇒ln…

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Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

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

A: Image is attached with detailed solution.

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A: According to the given information,

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A: The amount of decay of the radioactive element is given as follows. y=y0e-0.04t where t is the time…

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

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Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

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Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A: please comment if you need clarification. if you find my answer useful put thumbs up. Thank you.

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.