N2026 P1 Q2

An athlete is running in an ultramarathon race. The distance travelled by the athlete is modelled by the following.

• In the first \(15\) minutes she runs a distance of \(2.5\text{ km}\).
• In subsequent \(15\)-minute time intervals she runs \(95\%\) of the distance she ran in the previous \(15\)-minute time interval.

1. According to the model, find the distance she runs between \(1\) hour and \(1\) hour \(15\) minutes after the start.[1]

The total distance of this ultramarathon is \(52\text{ km}\).

2. According to the model, find the \(15\)-minute time interval in which the athlete will reach the half-way point.[3]
3. According to the model, determine whether she will complete the ultramarathon, and hence explain whether the model is suitable.[3]