The amount of radioactive radium, whose half-life is 1620 years, remaining after t years, is given by the formula below. If the initial sample contains 45 grams

Q: A scientist puts 250 grams of radioactive radium having a half-life of 1690 years into a concrete…

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Q: A radioactive substance has a half-life of 1620 years. if its mass is now 15 grams, how much will be…

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Q: How many years will it take a $815 investment to be worth $1,392 if it continuously compound at 7%…

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Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

Q: How long (in years) will it take a $300 investment to be worth $400 if it is continuously compounded…

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Q: An initial investment of $4800 earns 8.7% interest, compounded continuously. What will the…

A: Given,          P=$4800r =8.7%t = 12 years

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

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Q: Second National Bank offers an account that earns 4.70% per year, compounded continuously. If a…

A: When annual interest is compounded continuously;         P(n)= P0*(er*n) where, P(n)= value at time…

Q: The population of a southern city follows the exponential law. If the population doubled in size…

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Q: A scientist puts 200 grams of radioactive radium having a half-life of 1690 years into a concrete…

A: Radioactive decay

Q: The doubling time of an investment is the amount of time it takes to double in value. If an…

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Q: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

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Q: The half-life of radium is 1690 years. If 10 grams is present now, how much will be present in 100…

A: Half life of radium is 1690 years Present mass = 10 grams Mass at 100 years from now is to be…

Q: If a certain substance exponentially decays from 100 grams to 20 grams in 3 years. How much of the…

A:

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.4 grams of carbon-14 to be…

A: We have to find

Q: How much money invested at 5 % compounded continuously for 3 years will yield $ 820

A: Given:  Rate of interest(r)    = 5%  = 0.05 (continuous compounding) Future amount(FV)  = $820 time…

Q: How much money invested at 5% compounded continuously for 3 years will result in $82

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Q: It will take _____ years to double.    How long will it take if the interest is compou

A: Compound interest: $3,800 to double if it is invested at 8% annual interest compounded 2 times a…

Q: The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to…

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Q: If 250mg of a radioactive element decays to 190mg in 12 hours, find the half-life of the…

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Q: A person invested $5, 600 in an account growing at a rate allowing the money to double every 6…

A: Consider the initial amount is $5600 The doubling time is 6 years The general form for the growth…

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: The half-life of carbon-14 is 5,730 years. If there are 600 grams of carbon-14 in a tree when it is…

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Q: If $8000 is invested at 5% compounded continuously, what is the amount after 3 years? The amount…

A: According to the given information, it is required to calculate the amount after 3 years.…

Q: The half-life of carbon-14 is 5730 years. How long does it take for 3.9 grams of carbon-14 to be…

A: h=5730 years. x=final amount=1.7 grams. y=initial amount=3.9 grams. t=h(ln(x/y))/ln(1/2)…

Q: A radioactive substance has a half-life of 3000 years. If you start with 100 kg of it, how much will…

A: In 1 half life amount becomes half of its initial value. After n half life it becomes 1/2n of its…

Q: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

A: Given: The half-life of carbon-14 is 5600 years. If a piece of charcoal is made from the wood of a…

Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

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Q: The half-life of radium is 1690 years. If 10 grams is present now, how much will be present in 50…

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Q: A man with ​$30,000 to invest decides to diversify his investments by placing $15,000 in an account…

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Q: How long $2,700 should be invested at 4.5% compounded continuously to grow $5,803

A:

Q: The half-life of silicon-32 is 710 years. If 70 grams is present now, how much will be present in…

A: The equation governing mass at any time t will be: m(t) = m0e-kt where k = 0.693 / t1/2 = 0.693 /…

Q: If 3000 dollars is invested in a bank account at an interest rate of 9 per cent per year, compounded…

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Q: If 50 grams of a radioactive substance decomposed to 42 grams in 2 years, then, to the nearest gram…

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Q: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

A: The half-life formula is given by: y=a(b)th...(1) where y is the final amount, a is the initial…

Q: If 100 grams of a radioactive material diminish to 80 grams in 2 years, find the half-life of the…

A: Let the given condition can be modeled as  y=y0eλt   where, y=  Final quantity y0= Initial quantity…

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A:

Q: It has been estimated that the world's tropical rain forests are disappearing at the rate of 1.8%…

A: To Determine:  how soon will the rain forests be reduced to 25% of their present size? Given: It has…

Q: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

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Q: A bank note will be worth $86,500 when it matures in 7 years. If the note pays 4.76% per year…

A:

Q: The half-life of Carbon-29 is 1300 years. If 15 grams are present now, how much will be present in…

A: Let A(t) be the amount of Carbon-29 remaining in t years, then

Q: A bank note will be worth $75,500 when it matures in 5 years. If the note pays 4.96% per year…

A: Recall the following fact.

Q: Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 4 yr if…

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Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Let us assume it takes n half-lifes to reach 10mg

Q: A person invested $3, 700 in an account growing at a rate allowing the money to double every 14…

A: we need to find the yearly compound interest rate then we will find the years taken for the value to…

Q: What amount needs to be invested today at 4% simple interest in order to have $6000 in 3 years?

A:

Q: What present value amounts to $21,204.90 if it is invested for 6 years at 7% compounded every 4…

A: A=P1+rnnt

Q: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

A: The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year)…

Q: A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

A: Given:A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…