If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint: The amount goes from A 0 to in 7,300 years.)

Q: 3. An account with an initial deposit of $6,500 earns 7.25% annual interest, compounded…

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Q: Determine whether the following statement is true or false, and explain why. The half-life of a…

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Q: If you make an investment of $2,000 and the interest is compounded continuously at 3%, approximately…

A: There are multiple question. As per company policy ask other question separately. Formula for…

Q: To provide for a future expansion, a company plans to make continuous deposits to a savings account…

A: A differential equation is an equation that usually relates a function with with its derivatives.…

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 3% compounded continuously, what is the amount after 3 years? The amount…

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Q: Find the present value for a $90,000 investment for 24 years at a compounded continuously at 4.1%.

A: P=Aert Where P is present value , A is amount and r is rate and t is time.

Q: Verify that the half-life of a quantity that decays exponentially with decay constant k is equal to…

A: Given : Quantity decays exponentially with constant decay constant k. The standard exponential…

Q: How long, to the nearest year, will it take an investment to double if it is continuously compounded…

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Q: At what nominal rate compounded continuously must money be invested to triple in 7 years? ..... A…

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Q: A survey estimates the current average cost of college to be $33,245per year.   ​(a) If the average…

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Q: A sample of tritium-3 decayed to 94.5% of its originalamount after a year.(a) What is the half-life…

A: A sample of tritium-3 decayed to 94.5% of its original amount after a year. We have to find (a) What…

Q: A culture of bacteria obeys the law of natural exponential growth. If 140,000 bacteria are present…

A: We can make it easier for you.

Q: How long, to the nearest year, will it take an investment to double if it is continuously compounded…

A:

Q: Suppose that a chemical reaction proceeds according to the law of growth and decay. If half the…

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Q: At current growth rates, the earth’s population is doubling about every 69 years. If this growth…

A: Number  of years - To calculate

Q: 2. Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

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Q: find the present value of 4,000 to be received in 5 years, if money may be invested at 7.1% with…

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Q: The population of minnows in the lagoon is 5,400, but the population will decay exponentially. If…

A: The formula for the exponential decay model is, y=C1-rt Here, y is the final amount C is the initial…

Q: If the present value of $1000 to be received in 5 years is $548.80, what rate of interest,…

A: Given values Present value, P=$1000 time, t=5 years Amount, A=$548.80 For calculating rate of…

Q: If the quantity of a substance decreases by 4% in 11 hours, find its half-life. Round constants to…

A: Let initial quantity is A0 . Quantity after t hours = Ak= some constant.A is given by:

Q: How many years are required for an investment to double in value if it is appreciating at the yearly…

A: The final amount when it is compounded continuously is given by  A=P0ert Where r = interest rate…

Q: A scientist wants to determine the halflife of a certain radioactive substance. She determines that…

A: The half life function is given by: N(t)=N0(0.5)t/t1/2 where N(t) is the final amount in milligrams…

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: 4. The population of the world is expected to double in the next 30 yr. What is its growth rate?

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Q: If $2000 is invested at 6% interest, find the amounts due to the nearest cent at the end of 4 years…

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Q: explain this.  How long will it take Dio who has an investment  of $200 at 4% interest compounded…

A: Given:

Q: How much money needs to be deposited now into an account to obtain $1,700 in 5 years if the interest…

A: Total amount of money at the end of nth  year is given by,                               A = P 1 +…

Q: Find the present value for a $85,000 investment for 11 years at a compounded continuously at 3.2%.

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Q: If the half-life of a radioactive substance is 6,800 years, then at what rate is it decaying? (Hint:…

A:

Q: 7. At what interest rate compounded continuously must money be invested in order to triple in 10…

A: We know that  P=Aert where A= Principal value r=rate  and t=time

Q: Suppose that the half-life of a substance is 250 years. If there were initially 100 g of the…

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Q: 9. If you invest $2500 at 2.8% compounded continuously how much will you have at the end of 10…

A:

Q: Given an interest rate of 7.2% per year, compounded continuously. What is the quarterly interest…

A: Given query is to find the quarterly intrest rate.

Q: Suppose a population of insects increases according to the law of exponential growth. There were 130…

A: Since the population increases by law of exponential growth.

Q: If the half-life of a radioactive substance is 6,700 years, then at what rate is it decaying? 1…

A: The decay law is given by, A(t)=A0e-kt Where, A0 is the amount at t=0. And, t1/2=ln2k

Q: suppose $5,000 is invested in an account at an annual interest rate of 3.7% compounded continuously.…

A: Given,

Q: 16) How long, to the nearest year, will it take an investment to triple if it is continuously…

A:

Q: How much money must be invested now at 10% interest compounded continuously so that $120, 000 will…

A:

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A:

Q: If an initial population of 32 grows exponentially at a rate of 50% per year, then what will the…

A: Given,          An initial population of 32 grows exponentially at a rate of 50% per year.We know…

Q: At what interest rate compounded continuously must money be invested to double in 4 years? A rate of…

A: Use formula of compounded continuously

Q: Adrian is going to invest $9,900 and leave it in an account for 10 years. Assuming the interest is…

A: Simply use the formula for compound interest.

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: The radioactive decay is modelled using the equation, N(t)=N0e-kt. Here, N(t) is the amount of…

Q: A population is now 3000 and is growing exponentiallywith a growth constant of .02, what will be the…

A:

Q: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

A:

Q: How long will it take for an investment to triple, if interest is compounded continuously at 6%? It…

A: Given

Q: 2. At what rate of interest, compounded continuously will an investment double in six years? 3.…

A: (2) given that the principle amount will gets doubled in six years if the amount is compounded…

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

A: We have to find how fast balance will grow per year after 4 year

Q: If a population of is becoming extinct and the population is decaying exponentially. Assume that…

A: From given information

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.