Problem 118 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My body temperature is a function of the time of day.

Step-by-Step Solution

Answer

Yes, the statement makes sense. In a regular and healthy routine, body temperature can be considered a function of the time of day, due to the body’s natural circadian rhythm. However, it's important to consider there are other factors that can affect body temperature as well.

Step 1: Confirm the parameters of the statement

The statement says 'My body temperature is a function of the time of day.' This statement is talking about a possible relationship between body temperature('Output') and the time of day('Input'). Everyone’s body temperature varies slightly during the course of the day - usually cooler in the early morning and warmer in the afternoon and evening. A function is a special relationship where each input into a process is related to exactly one output. In other words, for every 'Input' (time of day), there is exactly one 'Output' (body temperature).

Step 2: Apply basic principles of functions

Looking at the statement in the light of how functions operate, 'time of day' is our input variable and 'body temperature' is our output variable. At any particular 'time of day' there should be exactly one corresponding 'body temperature'.

Step 3: Analyze the statement

Now, analyzing this statement and knowing that body temperature changes over the course of a day, it could be said that body temperature is a function of the time of day. It is reasonable to anticipate this correlation due to the body's natural circadian rhythm. However, it is important to recognize that other factors could also affect our body temperature, such as illness, exercise, hot drinks, etc. Notwithstanding these, on a regular healthy day with normal activity, body temperature can be predicted by time.