Question

Thomas starts a canned food collection with 2 cans of food. He challenges his friends to bring 4 cans on the second day, 8 cans on the third day, and 16 cans on the fourth day. Thomas and his friends plan to collect cans for 10 days. Which statement describes why the relation between the number of days and the cans collected is a function?

A) For each day, there's exactly one amount of cans collected.
B) The number of cans collected increases exponentially each day.
C) There's no specific relation between days and cans collected.
D) The number of days and cans collected does not have a pattern.

Answer 1

The relationship between days and cans collected is a function because each day corresponds to one specific amount of cans, fulfilling the criterion of a function with unique inputs and outputs.

Step-by-step explanation:

The relation between the number of days and the cans collected in Thomas's canned food collection is a function because for each day, there is exactly one amount of cans collected. This satisfies the definition of a function, where each input (in this case, each day) is associated with exactly one output (the number of cans collected on that day).

The amount of cans doubling each subsequent day means the relationship is exponential, but that alone does not define it as a function. A function does not require an exponential relationship; the key characteristic of a function is the unique association between inputs and outputs.