2024 ACJC Promo Q12

The school's step challenge is an initiative by the PE department to encourage students to lead more active lifestyles. The table below shows the corresponding daily step counts and the number of health points that can be earned.

Student \(A\) walks \(4500\) steps on the first day. For each subsequent day, he increases his step count by \(350\) steps from the previous day.

1. 1. On which day will Student \(A\) first earn \(15\) Health Points in one day?[2]
   2. How many Health Points would Student \(A\) earn by the end of the \(20\)th day?[3]

Student \(B\) walks \(7500\) steps on the first day. For each subsequent day, he increases his step count by \(x \%\) from the previous day.

3. 1. Student \(B\) would like to complete a total of at least \(261,500\) steps in the first \(20\) days. Find the minimum value of \(x\), giving your answer correct to \(2\) decimal points.[3]
   2. Given that \(x = 3.80\), find the total number of health points that Student \(B\) can earn in \(20\) days.[3]

4. A student earns a \(\$2\) coupon for completing at least \(10,000\) steps on Day \(1\). For each subsequent day, the student will earn a new coupon and the value of each new coupon decreases by \(9 \%\) from the value of the previous day's coupon. If the student consistently completes \(10,000\) steps every day, show that the total coupon value accumulated over time will not exceed \(\$23\).[2]