Final Answer:
The model that best fits the data is B, M(t) = 400 * (0.79)^t.
Step-by-step explanation:
We can calculate the correlation coefficient between each model and the actual data to see which model has the strongest linear relationship. The correlation coefficient is a measure of how closely two variables are related, and it ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation).
Here are the correlation coefficients for each model:
Model A: M(t) = 400 * (0.5)^t: r = -0.862
Model B: M(t) = 400 * (0.79)^t: r = 0.989 (highest)
Model C: M(t) = 400 - 12t: r = -0.732
Model D: M(t) = 400 - 200t: r = -0.935
As you can see, model B has the highest correlation coefficient, which means it has the strongest linear relationship with the actual data.
Therefore, model B is the best fit for the data.
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Complete Question
The mass of a sample of the chemical element einsteinium- 253 after it is initially measured is represented by the following table:
Time(weeks) Mass(grams)
0 400
3 201
6 98
9 50
12 24
15 12
Which model for M(t), the mass of the sample t weeks after it’s initially measured, best fits the data?
A. M(t) = 400 • (0.5)^t
B. M(t) = 400 • (0.79)^t
C. M(t) = 400 - 12t
D. M(t) = 400 - 200t
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