Math Problem Statement

only answers for each no work please

Generate a table of values to estimate the half-life of a substance that decays according to the function y = 100 * 0.7^x, where x is the number of time periods, each time period is 12 hours, and y is in grams.

Solution

Here are the answers based on the provided decay function y=100⋅0.7xy = 100 \cdot 0.7^x:

Table of Values (Rounded to Two Decimal Places):

Time Period (x)Amount (y in grams)
0100.00
170.00
249.00
334.30
424.01
516.81
611.77
78.24
85.76
94.03
102.82

Additional Answers:

  • The half-life is a little less than: 18 hours.
  • It takes a little more than: 60 hours for the substance to weigh less than 4 grams.

Would you like more details on any part of this?

Here are some additional questions that could deepen your understanding:

  1. How do you calculate the half-life using the decay formula?
  2. What happens to the value of yy as xx increases indefinitely?
  3. How does changing the decay factor (0.7) affect the half-life of the substance?
  4. How is the decay formula related to exponential functions?
  5. Why is it necessary to round the values in a scientific context?

Tip: For exponential decay problems, remember that the half-life represents the time it takes for a substance to reduce to half its initial amount.

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Math Problem Analysis

Mathematical Concepts

Exponential Decay
Half-Life
Algebra

Formulas

y = 100 * 0.7^x

Theorems

-

Suitable Grade Level

Grades 9-11

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