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Mathematics LibreTexts

16.3: Exercises

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Exercise 16.3.1

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

It takes 49.262 minutes until 2 mg are left of the element.

Exercise 16.3.2

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

2.29 grams are left after 1 year.

Exercise 16.3.3

Fermium-252 decays in 10 minutes to 76.1% of its original mass. Find the half-life of fermium-252.

Answer

The half-life of fermium-252 is 25.38 minutes.

Exercise 16.3.4

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

You have to wait approximately 101.3 days.

Exercise 16.3.5

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

67.8% of the carbon-14 is left in the year 2000.

Exercise 16.3.6

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

The wood is approximately 3323 years old

Exercise 16.3.7

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

The bone is approximately 3952 years old.

Exercise 16.3.8

An investment of $5,000 was locked in for 30 years. According to the agreed conditions, the investment will be worth $5,0001.08t after t years.

  1. How much is the investment worth after 5 years?
  2. After how many years will the investment be worth $20,000?
Answer
  1. $7,346.64
  2. It takes approximately 18 years

Exercise 16.3.9

Determine the final amount in a savings account under the given conditions.

  1. $700,& compounded quarterly, & at 3%, & for 7 years
  2. $1400,& compounded annually, & at 2.25%, & for 5 years
  3. $1400,& compounded continuously, & at 2.25%, & for 5 years
  4. $500,& compounded monthly, & at 3.99%, & for 2 years
  5. $5000,& compounded continuously, & at 7.4%, & for 3 years
  6. $1600,& compounded daily, & at 3.333%, & for 1 year
  7. $750,& compounded semi-annually, & at 4.9%, & for 4 years
Answer
  1. $862.90
  2. $1,564.75
  3. $1,566.70
  4. $541.46
  5. $6,242.86
  6. $1,654.22
  7. $910.24

Exercise 16.3.10

  1. 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.
  2. Find the present value P of a future amount of A=$3500 invested at 6% compounded annually for 3 years.
  3. Find the present value P of a future amount of $1000 invested at a rate of 4.9% compounded continuously for 7 years.
  4. At what rate do we have to invest $1900 for 4 years compounded monthly to obtain a final amount of $2250?
  5. At what rate do we have to invest $1300 for 10 years compounded continuously to obtain a final amount of $2000?
  6. For how long do we have to invest $3400 at a rate of 5.125% compounded annually to obtain a final amount of $3700?
  7. For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a final amount of $1100?
  8. How long do you have to invest a principal at a rate of 6.75% compounded daily until the investment doubles its value?
  9. 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
  1. P=$1,484.39
  2. P=$2,938.67
  3. P=$709.64
  4. r=4.23%
  5. r=4.31%
  6. t1.69 years
  7. t3.81 years
  8. t10.27 years
  9. t13.73 years

This page titled 16.3: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform.

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