0.5 Mathematical models  (Page 2/3)

When an object is dropped or thrown downward, the distance, $d$ , that it falls in time, $t$ is described by the following equation:

In this equation, $v_0$ is the initial velocity, in m $·$ s ${}^{-1}$ . Distance is measured in meters and time is measured in seconds. Use the equation to find how far an object will fall in 2 s if it is thrown downward at an initial velocity of 10 m $·$ s ${}^{-1}$ .

When an object is dropped or thrown downward, the distance, $d$ , that it falls in time, $t$ is described by the following equation:

In this equation, $v_0$ is the initial velocity, in m $·$ s ${}^{-1}$ . Distance is measured in meters and time is measured in seconds. Use the equation find how long it takes for the object to reach the ground if it is dropped from a height of 2000 m. The initial velocity is 0 m $·$ s ${}^{-1}$ .

A researcher is investigating the number of trees in a forest over a period of n years. After investigating numerous data, the following data model emerged:

1. How many trees, in hundreds, are there in the SIXTH year if this pattern is continued?
2. Determine an algebraic expression that describes the number of trees in the $n^{th}$ year in the forest.
3. Do you think this model, which determines the number of trees in the forest, will continue indefinitely? Give a reason for your answer.