Question

there is a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. for a certain type of cricket, this relationship can be represented using the formula $t = 0.2c + 40$, where $t$ represents the temperature in degrees fahrenheit and $c$ represents the number of times the cricket chirps in one minute. what is the meaning of the $c$ value when $t = 0$?

answer

the change in temperature in degrees fahrenheit for each additional cricket chirp in one minute.
the expected temperature in degrees fahrenheit if the cricket has chirped 0 times per minute.
the number of times the cricket could be expected to chirp in one minute if its 0°f.
the expected temperature in degrees fahrenheit if the cricket has chirped 40 times per minute.

Explanation:

Step1: Recall the formula

We have the linear formula \( T = 0.2c + 40 \), and we need to find the meaning of \( c \) when \( T = 0 \) (though in reality, temperature can't be 0 here in context, but mathematically we solve). Wait, actually, the question is about the meaning of the \( c \)-value when \( T = 0 \)? Wait, no, maybe a typo? Wait, the formula is \( T = 0.2c + 40 \). Let's solve for \( c \) when \( T = 0 \) (even if unrealistic, mathematically):

Step2: Substitute \( T = 0 \) into the formula

Substitute \( T = 0 \) into \( T = 0.2c + 40 \):
\( 0 = 0.2c + 40 \)

Step3: Solve for \( c \)

Subtract 40 from both sides: \( -40 = 0.2c \)
Divide both sides by 0.2: \( c = \frac{-40}{0.2} = -200 \)

But in context, the formula \( T = 0.2c + 40 \) models temperature \( T \) (°F) and chirps \( c \) per minute. The \( c \)-value when \( T = 0 \) (mathematically) would represent the number of chirps per minute when the temperature is 0°F (even though crickets don't chirp at 0°F, but in the linear model, it's the theoretical \( c \) when \( T = 0 \)). Wait, but looking at the options, one option is "One number of times the cricket could be expected to chirp in one minute if it's 0°F" (paraphrasing). Let's check the options:

Wait, the options (from the image, though text is a bit unclear) – one option is "One number of times the cricket could be expected to chirp in one minute if it's 0°F" (the third option? Wait, the user's image has options:

1. The change in temperature...
2. The expected temperature...
3. One number of times the cricket could be expected to chirp in one minute if it's 0°F
4. The expected temperature...

Wait, when we solve \( T = 0.2c + 40 \) for \( c \) when \( T = 0 \), we get \( c = -200 \), but the meaning is: the number of chirps per minute (c) when the temperature (T) is 0°F. So the option "One number of times the cricket could be expected to chirp in one minute if it's 0°F" (the third option, maybe labeled as "One number of times the cricket could be expected to chirp in one minute if it's 0°F" – the third option in the list) is the meaning. Because we're finding c (chirps per minute) when T (temperature) is 0°F.

Answer:

The option: "One number of times the cricket could be expected to chirp in one minute if it's 0°F" (the third option in the list of options provided, likely the one with text about chirps at 0°F)