Question
The equation that best models the linearized data for a particular data set is log y equals 0.0169217 x plus 1.44908. Find the approximate value of y when x = 26. Round your answer to the nearest whole number.
(1 point)
Responses
2
2
77
77
579
579
760
(1 point)
Responses
2
2
77
77
579
579
760
Answers
GPT-4o mini
To find the value of \( y \) when \( x = 26 \), we start from the given equation:
\[
\log y = 0.0169217 x + 1.44908
\]
Now, we can substitute \( x = 26 \) into the equation:
\[
\log y = 0.0169217(26) + 1.44908
\]
Calculating the term \( 0.0169217 \times 26 \):
\[
0.0169217 \times 26 = 0.4407922
\]
Now, we add this result to 1.44908:
\[
\log y = 0.4407922 + 1.44908 = 1.8898722
\]
Next, to find \( y \), we need to convert from logarithmic form to standard form:
\[
y = 10^{\log y} = 10^{1.8898722}
\]
Now we take \( 10^{1.8898722} \):
Calculating \( 10^{1.8898722} \):
\[
y \approx 77.08
\]
Rounding to the nearest whole number, we get:
\[
y \approx 77
\]
Thus, the approximate value of \( y \) when \( x = 26 \) is \( \boxed{77} \).
\[
\log y = 0.0169217 x + 1.44908
\]
Now, we can substitute \( x = 26 \) into the equation:
\[
\log y = 0.0169217(26) + 1.44908
\]
Calculating the term \( 0.0169217 \times 26 \):
\[
0.0169217 \times 26 = 0.4407922
\]
Now, we add this result to 1.44908:
\[
\log y = 0.4407922 + 1.44908 = 1.8898722
\]
Next, to find \( y \), we need to convert from logarithmic form to standard form:
\[
y = 10^{\log y} = 10^{1.8898722}
\]
Now we take \( 10^{1.8898722} \):
Calculating \( 10^{1.8898722} \):
\[
y \approx 77.08
\]
Rounding to the nearest whole number, we get:
\[
y \approx 77
\]
Thus, the approximate value of \( y \) when \( x = 26 \) is \( \boxed{77} \).