Question

A student collected monetary pledges for a fundraiser. One donor pledged to contribute $5 for each mile walked by the student during the fundraising walk up to a maximum of six miles.

A. is the situation continuous or discrete
B.write the domain and range of the situation

Answer 1

A. The situation is discrete B. i. { x : 0 ≤ x ≤ 6; x ∈ Z} ii. { C = 5x : 0 ≤ C ≤ 30; C ∈ Z}

Explanation:

A. The situation is discrete since we have integral values for the amount paid per mile walked. The amount per mile is $5 and is only paid if a complete mile is walked. So, it is a discrete situation.

B. i. Since 0 miles represents 0 distance and the student walks a maximum of 6 miles, let x represent the distance walked. So the domain is 0 ≤ x ≤ 6 where x ∈ Z where Z represent integers.

{ x : 0 ≤ x ≤ 6; x ∈ Z}

ii. Since at 0 miles the amount earned is 0 miles × $5 per mile = $ 0 and at the maximum distance of 6 miles, the amount earned is 6 miles × $5 per mile = $ 30, let C represent the amount donated in dollars. So the range is 0 ≤ C ≤ $ 30 where C = 5x.

{ C = 5x : 0 ≤ C ≤ 30; C ∈ Z}