Mr. Hughes is competing in the Mr. Legs campaign to raise money for the Coral Shores High School scholarship fund. On the first day, he collected 2 dollars. On the third day, he collected $8. Let D represent each collection day and N represent the number of dollars collected on that day. Matt claims that the situation can be modeled by an exponential function. Emily disagrees and claims that the number of dollars collected can be modeled by a linear function.

Question

Mr. Hughes is competing in the Mr. Legs campaign to raise money for the Coral Shores High School scholarship fund. On the first day, he collected 2 dollars. On the third day, he collected $8. Let D represent each collection day and N represent the number of dollars collected on that day. Matt claims that the situation can be modeled by an exponential function. Emily disagrees and claims that the number of dollars collected can be modeled by a linear function.

Which statement is true about the number of dollars predicted to be collected on the 6th day based on the two models?

Answer 1

Based on the information provided, since Mr. Hughes collected $2 on the first day and $8 on the third day, we can see that the amounts collected are not growing exponentially, as the increase is not consistent. This suggests that Emily is correct in her claim that the number of dollars collected can be modeled by a linear function.

If the amount collected is modeled by a linear function, then the amount collected each day increases by a consistent amount. Therefore, to predict the amount collected on the 6th day, we can find the difference in the amounts collected on the first and third day, which is $8 - $2 = $6.

So, if Mr. Hughes continues to collect money at a consistent rate, he would be expected to collect $6 more on the 4th, 5th, and 6th days. Therefore, on the 6th day, he would collect $8 + $6 + $6 = $20.