16.3: Exercises
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An unstable element decays at a rate of 5.9% per minute. If 40mg of this element has been produced, then how long will it take until 2mg of the element are left? Round your answer to the nearest thousandth.
- Answer
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It takes 49.262 minutes until 2 mg are left of the element.
A substance decays radioactively with a half-life of 232.5 days. How much of 6.8 grams of this substance is left after 1 year?
- Answer
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2.29 grams are left after 1 year.
Fermium-252 decays in 10 minutes to 76.1% of its original mass. Find the half-life of fermium-252.
- Answer
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The half-life of fermium-252 is 25.38 minutes.
How long do you have to wait until 15mg of beryllium-7 have decayed to 4mg, if the half-life of beryllium-7 is 53.12 days?
- Answer
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You have to wait approximately 101.3 days.
If Pharaoh Ramses II died in the year 1213 BC, then what percent of the carbon-14 was left in the mummy of Ramses II in the year 2000?
- Answer
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67.8% of the carbon-14 is left in the year 2000.
In order to determine the age of a piece of wood, the amount of carbon-14 was measured. It was determined that the wood had lost 33.1% of its carbon-14. How old is this piece of wood?
- Answer
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The wood is approximately 3323 years old
Archaeologists uncovered a bone at an ancient resting ground. It was determined that 62% of the carbon-14 was left in the bone. How old is the bone?
- Answer
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The bone is approximately 3952 years old.
An investment of $5,000 was locked in for 30 years. According to the agreed conditions, the investment will be worth $5,000⋅1.08t after t years.
- How much is the investment worth after 5 years?
- After how many years will the investment be worth $20,000?
- Answer
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- $7,346.64
- It takes approximately 18 years
Determine the final amount in a savings account under the given conditions.
- $700,& compounded quarterly, & at 3%, & for 7 years
- $1400,& compounded annually, & at 2.25%, & for 5 years
- $1400,& compounded continuously, & at 2.25%, & for 5 years
- $500,& compounded monthly, & at 3.99%, & for 2 years
- $5000,& compounded continuously, & at 7.4%, & for 3 years
- $1600,& compounded daily, & at 3.333%, & for 1 year
- $750,& compounded semi-annually, & at 4.9%, & for 4 years
- Answer
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- $862.90
- $1,564.75
- $1,566.70
- $541.46
- $6,242.86
- $1,654.22
- $910.24
- Find the amount P that needs to be invested at a rate of 5% compounded quarterly for 6 years to give a final amount of $2000.
- Find the present value P of a future amount of A=$3500 invested at 6% compounded annually for 3 years.
- Find the present value P of a future amount of $1000 invested at a rate of 4.9% compounded continuously for 7 years.
- At what rate do we have to invest $1900 for 4 years compounded monthly to obtain a final amount of $2250?
- At what rate do we have to invest $1300 for 10 years compounded continuously to obtain a final amount of $2000?
- For how long do we have to invest $3400 at a rate of 5.125% compounded annually to obtain a final amount of $3700?
- For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a final amount of $1100?
- How long do you have to invest a principal at a rate of 6.75% compounded daily until the investment doubles its value?
- An certain amount of money has tripled its value while being in a savings account that has an interest rate of 8% compounded continuously. For how long was the money in the savings account?
- Answer
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- P=$1,484.39
- P=$2,938.67
- P=$709.64
- r=4.23%
- r=4.31%
- t≈1.69 years
- t≈3.81 years
- t≈10.27 years
- t≈13.73 years