The equation of Celia's exponential model is [tex]y = 9.4 * 0.75^x[/tex]
How to estimate the model?
The table that completes the question is added as an attachment
The y-intercept is given as:
(0,9.4)
The ratios of successive data values are calculated as:
[tex]r_1 = \frac{6.0}{10}= 0.6[/tex]
[tex]r_2 = \frac{5.4}{6.0}= 0.9[/tex]
[tex]r_3 = \frac{3.9}{5.4}= 0.72[/tex]
[tex]r_4 = \frac{3.7}{3.9}= 0.95[/tex]
[tex]r_5 = \frac{2.3}{3.7}= 0.62[/tex]
[tex]r_6 = \frac{1.4}{2.3}= 0.61[/tex]
[tex]r_7 = \frac{1.0}{1.4}= 0.71[/tex]
[tex]r_8 = \frac{0.9}{1.0}= 0.9[/tex]
[tex]r_9 = \frac{0.8}{0.9}= 0.89[/tex]
[tex]r_{10} = \frac{0.5}{0.8}= 0.63[/tex]
The average of the above values is
[tex]b = \frac{0.6 + 0.9 + 0.72 + 0.95 + 0.62 + 0.61 + 0.71 + 0.9 + 0.89 + 0.63}{10}[/tex]
Evaluate
b = 0.75
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where
a = 9.4 as in the y-intercept (0,9.4)
b = 0.75
Substitute these values in [tex]y = ab^x[/tex]
[tex]y = 9.4 * 0.75^x[/tex]
Hence, the Celia's exponential model is [tex]y = 9.4 * 0.75^x[/tex]
Read more about exponential function at:
https://brainly.com/question/11464095
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