A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the value of the quantity after 10 weeks, to the nearest hundredth?

Q: If $4,000 is invested at 7% compounded continuously, how long will it take for it to grow to $6,000,…

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Q: 10. Engr. Igup invested P200 000 in a savin gs account with interest rate of 4% compounded…

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Q: If $6000 is invested at 3% compounded continuously, what is the amount after 8 years? The amount…

A: Answer  is   7625

Q: A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a)…

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Q: Of an initial amount of 6000 g of lead-210, how much will remain in 110 years? Lead-210 decays at a…

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Q: The half-life of Erbium-171 is 7.5 hours. What is the hourly decay rate? Express the result to four…

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Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

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

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100 mg…

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Q: If $5000 is invested at 8% compounded continuously, what is the amount after 3 years? The amount…

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Q: If $5000 is invested at 3% compounded continuously, what is the amount after 3 years? The amount…

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Q: 6. The radioactive isotope of lead, PB-209, decays at a rate proportional to the amount present at…

A: Let's find time to take 90% of the lead to decay.

Q: Camila invested $9,100 in an account paying an interest rate of 4.6% compounded continuously.…

A: Given problem:- Camila invested $9,100 in an account paying an interest rate of 4.6% compounded…

Q: If $35,000 is invested at 2.9% interest compounded continuously, how long will it take for the…

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Q: carbon-14? The decay​ rate, k, of​ carbon-14 is

A: The general exponential function of decaying is given as: A=A0e-kt where A is present amount Aο is…

Q: A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the…

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Q: If the half-life of a radioactive substance is 7,600 years, then at what rate is it decaying? 1…

A: We can find the rate of decay as below.

Q: of a radiooctive substonce decayed to 93.5% of its original sample amount after oyear What is the…

A: we need find half life substance k=? and t=?

Q: Of an initial amount of 5000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A:

Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: If $20,000 is invested in a savings account offering 3.5% per year, compounded continuously, how…

A: According to the question, we have to find the total amount after 3 years , If $20,000 is invested…

Q: 4.) The half-life of strontium-90 is 28 years. Find the rate of decay. How long will it take a 50 mg…

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Q: How long to the nearest year will it take $50,000 to triple in values at7.5% annual interest…

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Q: Find the accumulated amoust of P6,428 at the rate of 11% compounded continuously after 6 years.

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Q: It is found that 0.5% of radium disappears in 12 years, a.) What percent will disappear in 100…

A: We have to find the half life of the radium

Q: Suppose a sample of a certain substance decayed to 73.6% of its original amount after 300 days.…

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Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

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Q: If $6,000 is invested at 3% compounded continuously, what is the amount after 7 years? The amount…

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Q: How long will it take for 1000 to decay to 500 with a loss of 3% a year (approximate historical…

A: Given : Initial value = 1000 Final value = 500 Loss is 3% per year Apply the exponential decay…

Q: If $12, 000 is invested at a rate of 3% per year compounded continuously, find value of the…

A: The formula for continuously compounded interest is, A=Pert where P is the principal amount, r is…

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

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Q: Mr. Reyes places 100,000Php in a time deposit which pays nine percent per annum compounded…

A: topic - exponential function

Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 130 years? Lead-210 decays at a…

A: Find much much will remain

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

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Q: What initial investment at 8% compounded continuously for 5 years will accumulate to $50, 000?

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Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A: Given:             dAdt=k 0.043% of total amount has disintegrated :              =100-0.043%…

Q: A sample of a radioactive substance decayed to 10% of its original amount after 30 years. What is…

A: Given After 30 years substance decayed to 10 % of its original amount

Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: If ​$7000 is invested at 5​% compounded​ continuously, what is the amount after 7 ​years? round…

A: Given, Initial amount=$7000 Rate of interest=5%=0.05 Period=7years

Q: If $20,000 is invested at 2.8% compounded continuously, what is the amount in 5 years?

A: If $20,000 is invested at 2.8% compounded continuously, what is the amount in 5 years?

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: . How long, to the nearest year, will it take me to become a millionaire if I invest $1,000 at 10%…

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Q: Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that…

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Q: 2. The population of a suburb doubled in size in an 18-month peri growth continues and the current…

A: In this question we will use basic of calculus i.e application of differential equation. We will…

Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

Q: If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint:…

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Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

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.