UpStudy Free Solution:

To find the average walking speed of people living in Fairbanks, we need to use the given function \(R( P) = 0.37 \ln P + 0.05\) and substitute \(P\) with the population of Fairbanks in thousands.

The population of Fairbanks is 28,000, which is \(P = 28\) (since \(P\) is in thousands).

Now, substitute \(P = 28\) into the function:

\[R( 28) = 0.37 \ln 28 + 0.05\]

First, calculate \(\ln 28\):

\[\ln 28 \approx 3.3322\]

Now, multiply by 0.37:

\[0.37 \times 3.3322 \approx 1.2339\]

Add 0.05:

\[1.2339 + 0.05 = 1.2839\]

Rounding to the nearest tenth:

\[1.2839 \approx 1.3\]

Therefore, the average walking speed of people living in Fairbanks is \(1.3\) ft/sec.

Supplemental Knowledge

Logarithmic Functions

Logarithmic functions are the inverse of exponential functions. They are used to model various real-world phenomena, including growth rates and decay processes. The natural logarithm, denoted as \(\ln \), is a logarithm with base \(e\) (where \(e \approx 2.71828\)).

Function Evaluation

To evaluate a function at a given point:

1. Substitute the given value into the function.

2. Perform the necessary arithmetic operations.

In this problem, we are given the function:

\[R( P) = 0.37 \ln P + 0.05\]

where \(P\) is in thousands.

Join millions in excelling academically with UpStudy today - your ultimate partner for academic success!