Math Problem Statement

Strontium 90 is a radioactive material that decays according to the function

A(t)=A0e^−0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium-90.

a) the decay rate of strontium-90 is __%

b)approximately ___ grams of strontium 90 is left after 10 years

c) Only 100 grams of strontium-90 will be left in about ___ years

d)The half-life of strontium-90 is approximately ___ years 

round final answers to the nearest tenth as needed 

(no steps just answer)

Solution

a) 2.44%

b) 311.1 grams

c) 56.8 years

d) 28.4 years

Would you like details or have any questions?

Here are 5 questions you might want to ask:

  1. How do you derive the decay constant from the half-life of a substance?
  2. What is the formula for continuous exponential decay?
  3. Can you explain the relationship between half-life and decay rate?
  4. How do you calculate the remaining amount of a radioactive substance after a certain period?
  5. What are some real-world applications of understanding radioactive decay?

Tip: To solve problems involving exponential decay, familiarize yourself with the key parameters like the decay constant and the initial amount, and use the exponential decay formula effectively.

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Math Problem Analysis

Mathematical Concepts

Exponential Decay
Radioactive Decay

Formulas

A(t) = A0 * e^(-kt)

Theorems

-

Suitable Grade Level

Advanced High School or College

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