Question

Celia thinks that because the drop between the first two points is so large, the best model might actually have a y- intercept a little below 10. She uses (0, 9.4) to estimate a in her model. To estimate b, she finds the average of the ratios of successive data values. what is her model?use two digits for precision of all quantitites

Answer 1

The equation of Celia's exponential model is $y = 9.4 * 0.75^x$

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:

$r_1 = \frac{6.0}{10}= 0.6$

$r_2 = \frac{5.4}{6.0}= 0.9$

$r_3 = \frac{3.9}{5.4}= 0.72$

$r_4 = \frac{3.7}{3.9}= 0.95$

$r_5 = \frac{2.3}{3.7}= 0.62$

$r_6 = \frac{1.4}{2.3}= 0.61$

$r_7 = \frac{1.0}{1.4}= 0.71$

$r_8 = \frac{0.9}{1.0}= 0.9$

$r_9 = \frac{0.8}{0.9}= 0.89$

$r_{10} = \frac{0.5}{0.8}= 0.63$

The average of the above values is

$b = \frac{0.6 + 0.9 + 0.72 + 0.95 + 0.62 + 0.61 + 0.71 + 0.9 + 0.89 + 0.63}{10}$

Evaluate

b = 0.75

An exponential function is represented as:

$y = ab^x$

Where

a = 9.4 as in the y-intercept (0,9.4)

b = 0.75

Substitute these values in $y = ab^x$

$y = 9.4 * 0.75^x$

Hence, the Celia's exponential model is $y = 9.4 * 0.75^x$

Read more about exponential function at:

brainly.com/question/11464095

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