A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (seconds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x

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Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x