Answer
See explanation
Work Step by Step
Sure, let's solve it mathematically.
(a) To find the value of \( I \), we use the formula provided:
\[ I = T + \frac{5}{9}(6.11 \times e^{(5417.7530 \times (\frac{1}{273.16} - \frac{1}{(dewpoint+273.16))}})) \]
Given the actual temperature (\( T \)) and relative humidity (\( h \)), we can calculate \( I \).
(b) For what value of \( h \) is \( I = 80 \)? We need to solve the equation:
\[ 80 = T + \frac{5}{9}(6.11 \times e^{(5417.7530 \times (\frac{1}{273.16} - \frac{1}{(dewpoint+273.16))}})) \]
Given a specific temperature (\( T \)), solve for \( h \).
(c) For what value of \( h \) is \( I = 90 \)? Similar to (b), solve the equation for \( h \) given \( I = 90 \).
(d) To find the meanings of the functions \( I = f(T, h) \), and \( I = f(80, h) \), we analyze their behavior:
- \( I = f(T, h) \) represents the perceived temperature as a function of both actual temperature (\( T \)) and humidity (\( h \)). It shows how perceived temperature changes with variations in both temperature and humidity.
- \( I = f(80, h) \) represents the perceived temperature at a fixed actual temperature of 80 degrees. It shows how perceived temperature changes with varying humidity at a constant temperature of 80 degrees.
Comparing the behavior of these two functions helps understand how humidity affects perceived temperature at different fixed temperature levels.
