IB MATH AI SL, Paper 1, May, 2021, TZ2, Solved Past Paper

This question involves understanding the behavior of a medicinal drug in the body over time, modeled by an exponential decay function. The function given is $D(t)=23(0.85{)}^t$, where $D(t)$ represents the amount of the drug in milligrams at time $t$ hours after injection. Initially, before the injection, the amount of the drug in the body is zero. The function describes how the drug concentration decreases over time, with the base of the exponential function, $0.85$, indicating the rate at which the drug leaves the body. You are required to determine specific characteristics of this function, such as the initial dose and the rate of decay, as well as calculate the remaining amount of the drug after a certain period.

This question involves calculating distances and coordinates in a three-dimensional space, specifically for an inclined railway on a steep hill. The railway is represented by a straight track between two stations, A and B, with given coordinates in a 3D coordinate system. The x and y axes lie in the horizontal plane, while the z-axis is vertical, representing height above ground level. Station A is at ground level with coordinates $(140,15,0)$, and station B, near the top of the hill, is at $(20,5,250)$. The task is to find the distance between these two stations, the coordinates of a midpoint station M, and the height of station M above ground level.