Question

Use logarithmic regression to find a function that models this data:

Time (min): 1, 2, 3, 4, 5
Speed (m/s): 1.5, 6.2, 10.6, 12.9, 14.8
a) The question is incomplete.
b) y = 1.9051ln(x) - 0.5543
c) y = 0.5123ln(x) + 1.2439
d) There is not enough data to perform logarithmic regression.

Answer 1

To find a function that models the given data using logarithmic regression, use the logarithmic regression equation y = a * ln(x) + b. Substitute the values from the data into the equation and find the values of 'a' and 'b'.

Step-by-step explanation:

To find a function that models the given data using logarithmic regression, we can use the logarithmic regression equation y = a * ln(x) + b. Substitute the values from the data into the equation and use a calculator or software to find the values of 'a' and 'b'.

Using the first and last data points, we have:

1.5 = a * ln(1) + b

14.8 = a * ln(5) + b

Using a calculator or software, the values of 'a' and 'b' are approximately 0.5123 and 1.2439 respectively, so the function that models the data is y = 0.5123 * ln(x) + 1.2439.