Question

Find a logarithmic function to model the data.

x y

1 60


2 54


3 51


4 50


5 46


6 45


7 44




f(x) = 60.73(0.95)x Please help:(


f(x) = 0.93(60.73)x


f(x) = 60.04 – 8.25 ln x


f(x) = 8.25 – 60.04 ln x

Answer 1

f(x) = 60.04 – 8.25 ln x

Explanation:

A suitable calculator can find the regression formula coefficients for you.

f(x) = 60.04 – 8.25 ln(x)

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The attachment shows the calculator's computation of the model parameters (a₁ and b₁), and is also shows how these parameters might be calculated by hand (a₂ and b₂). The manual calculation involves taking the logarithms of the x-values and computing various means involving those and the y-values. These calculations are easily done on a graphing calculator or spreadsheet, but such a device will also likely be able to compute the regression equation for you.

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Comment on answer choices

You can eliminate the first two answer selections because these are not formulas that are logarithmic functions. You can eliminate the last choice because it models values near 8, not near 60. Thus, you can choose the correct answer without knowing much about how to make a logarithmic model.