Concept explainers
Radioactive Decay Strontium-90 is a radioactive material that decays according to the function , where is the initial amount present and is the amount present at time (in years). Assume that a scientist has a sample of 500 grams of strontium-90.
(a) What is the decay rate of strontium-90?
(b) Graph the function using a graphing utility.
(c) How much strontium-90 is left after 10 years?
(d) When will 400 grams of strontium-90 be left?
(e) What is the half-life of strontium-90?
To find:
a. What is the decay rate of strontium-90?
Answer to Problem 3AYU
Solution:
a.
Explanation of Solution
Given:
Calculation:
a. Compare where is a negative number that represents the rate of decay. We will get the values of as .
On converting the percentage,
Notation .
Therefore the decay rate of strontium-90 is .
To find:
b. Graph the function using a graphing utility.
Answer to Problem 3AYU
Solution:
b.
Explanation of Solution
Given:
Calculation:
b. Graph:
To find:
c. How much strontium-90 is left after 10 years?
Answer to Problem 3AYU
Solution:
c.
Explanation of Solution
Given:
Calculation:
c. Substitute 10 for and 500 for in the given function.
Therefore the amount of strontium 90 left after 10 years is about grams.
To find:
d. When will 400 grams of strontium-90 be left?
Answer to Problem 3AYU
Solution:
d.
Explanation of Solution
Given:
Calculation:
d. Substitute 400 for in the given function.
Taking log on both sides we get,
Therefore, 400 grams of strontium 90 will be left after about years.
To find:
e. What is the half-life of strontium-90?
Answer to Problem 3AYU
Solution:
e.
Explanation of Solution
Given:
Calculation:
e. Half life is the time required for half of the radioactive substance to decay. Since is the initial amount of strontium 90.
Replace in the given function.
Taking log on both sides we get,
Therefore, the half life of strontium 90 is years.
Chapter 5 Solutions
Precalculus
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