Question

theres a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside a certain type of cricket, this relationship can be expressed using the formula $t = 0.3c + 34$, where $t$ represents the temperature in degrees fahrenheit and $c$ represents the number of times the cricket chirps in a minute. what could the number 0.3 represent in the equation?

answer
the change in
temperature in degrees fahrenheit for each additional cricket chirp in one minute.
how long the cricket continues to chirp.
the expected temperature in degrees fahrenheit if the cricket has chirped 0.3 times per minute.
the change in cricket chirps per minute for each additional degree fahrenheit.

Explanation:

Step1: Recall linear equation form

The equation is in the form \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept. Here, \( T = 0.3c+34 \), so \( T \) is like \( y \), \( c \) is like \( x \), \( 0.3 \) is like \( m \), and \( 34 \) is like \( b \).

Step2: Interpret the slope

In a linear relationship \( y = mx + b \), the slope \( m \) represents the change in \( y \) for each unit change in \( x \). In our equation, \( T \) (temperature) is \( y \) and \( c \) (number of chirps per minute) is \( x \). So the slope \( 0.3 \) represents the change in \( T \) (temperature) for each unit change in \( c \) (each additional chirp per minute).

Now let's analyze the options:

• Option 1: "The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute." This matches the interpretation of the slope (rate of change of temperature with respect to chirps).
• Option 2: "How long the cricket continues to chirp." The equation has nothing to do with the duration of chirping, so this is incorrect.
• Option 3: "The expected temperature in degrees Fahrenheit if the cricket has chirped 0.3 times per minute." To find the temperature when \( c = 0.3 \), we use the equation, but the slope is not about the temperature at \( c = 0.3 \). So this is incorrect.
• Option 4: "The change in cricket chirps per minute for each additional degree Fahrenheit." The slope is about change in temperature with respect to chirps, not the other way around. So this is incorrect.

Answer:

The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.