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.
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