Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released into the air in a laboratory. If the resulting radiation level is 10% above the safe level, how long should the laboratory remain vacated? (Hint: To start with, determine what fraction of the "resulting radiation level" is the maximum safe level.) The laboratory should remain vacated for 0.548 days.

Q: Suppose a scientist has a fossil sample with 180 g (grams) of carbon-14. If its original amount of…

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Q: A small city has a population of 120,000 in 2010.  Concerned about rapid growth, the residents…

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Q: You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested…

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

A: Given: Half-life of radium = 1590 years To find: Time taken to disappear 1/4 of the radium. Formula…

Q: Suppose that $10,000 is invested and the account grows to $13,566.25 in 5 yr. a. Use the model A =…

A: The future value A and present value P for the time t years with continuous compounding rate is…

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

A: Given that Half life of radium is 1590 years To find How long would you have to wait for 1/8 of it…

Q: Given an interest rate of zero percent, the future value of a lump sum invested today wil always:…

A: Topic = Algebra OA. remain constant, regardless of the investment time period.

Q: Joshua is going to invest $680 and leave it in an account for 19 years. Assuming to interest is…

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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: A certain drug is eliminated from the bloodstream with a​ half-life of 34 hours. Suppose that a…

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Q: 9. If 75 mg of a radioactive substance decays to 15 mg in 20 years, find the Half-Life, in minutes,…

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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: How long would it take for a principal ofP to double if invested at 7% compounded continuously?

A: Given, for a principal of P to double if invested at 7% compounded continuously.

Q: If the national economy shrank at an annual rate of 9​% per year for three consecutive​ years, then…

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Q: A sample of radium has a weight of 1.5 mg and a half life of approximately 6 years. How much of the…

A: Given Data: The weight of the sample of radium is: W=1.5 mg The approximate half-life of the sample…

Q: A company estimates that 0.4% of their products will fail after the original warranty period but…

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Q: An investment of 6,000 grows at a rate of 4% for one year, then at a rate of 9% for three years.…

A: Investment amount = 6000 Rate of return for first year = 4% Rate of return for three years = 9% * 3…

Q: If the population of a small city is 45,000. If the population grows at a rate of 3% per year, in…

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Q: he population of greater Lafayette is increasing at a rate of .95% each year. If the population was…

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Q: How long, to the nearest hundredth of a year, would it take an initial principal P to triple if it…

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Q: If the price of gold decrease at a monthly rate of 2.1%, by what percentage does it decrease in a…

A: If something is decreasing at 2.1% per month,then after 1 month we have 100%-2.1%=97.9%so after each…

Q: Find the amount that results from the given investment. $10 invested at 9% compounded continuously…

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Q: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

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

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Q: Suppose you have $3000 to invest. Which investment yields the greater return over 10 years: 6.5%…

A: Let's consider the given scenarios:                          When the interest is compounded…

Q: You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested…

A: Given that: Yield is being reinvested quarterly, hence its quarterly compounding

Q: Suppose the half-life of a certain radioactive substance is 20 days and that there are5 grams…

A: Given that, The half-life of a certain radioactive substance is 20 days and that there are 5 grams…

Q: 2. Suppose a nuclear accident releases 50 kilograms of the element Cesium 137. If the half life of…

A: Given- Intial amount of Cesium-137 is 50 kg and half life is 30 years. To find- The amount after 30…

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Exponential decay formula: - The amount drops gradually, followed by a quick decrease in the rate of…

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: 1. A body at 50 degrees C cools inside a room with temperature of 30 degrees C. At what temperature…

A: Let's find.

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How long will it…

A: If A0 is initial amount present and T is half -life of the substance. Then the amount of substance…

Q: Suppose that a donor wishes to provide a cash gift to a hospital that will generate a continuous…

A: Given:- From the question , the annual rate of flow of the continuous income stream per year is ft=$…

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

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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: The growth rate of a certain strain of bacteria is unknown, but assumed to be constant. When an…

A: Given that the bacteria is growing at a constant rate. Initially there were 1500 bacteria and after…

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: Suppose that $12,000 is invested in a bond fund and the account grows to $14,309.26 in 4 yr.   a.…

A: (a) From the given information, it is observed that A = $14,309.26, P = $12,000 and t = 4.Compute…

Q: If $20,000 is invested at a rate of 5% per year compounded continuously, find the value of the…

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Q: The estimated value of a diamond purchased for investment purposes is determined by S(t) =…

A: Given:- Estimated value of a diamond is a function of timeS(t)=250(1.75)t14. rate of…

Q: In March 1976 the world population reached 5.5 billion. At that time, a popular news magazine…

A: Let's find.

Q: A sample of radium has a weight of 1.5mg and a half-life of approximately 6 years how much of the…

A:

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

A: Given, you have a cache of radium, which has a half-life of approximately 1590 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: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

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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. 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: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

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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.