Everything Maths Grade 11

10.3 CHAPTER 10. MATHEMATICAL MODELS

0

100

200

300

400

0 10 20 30 40

Time (s)

Distance (m)

1. How far does the cartravel in 20 s?


2. How long does it take the car to travel 300 m?

Example 3: More Mathematical Modelling

QUESTION

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

Year Number of trees (in hundreds)

1 1

2 3

3 9

4 27

1. How many trees, in hundreds, are there in thesixth year if this patternis continued?


2. Determine an algebraic expression that describes the number of trees in the nthyear in
   the forest.


3. Do you think this model, which determinesthe number of trees in the forest, will con-
   tinue indefinitely? Givea reason for your answer.

SOLUTION

Step 1 : Find the pattern

The pattern is 30 ;3^1 ;3^2 ;3^3 ;...

Therefore, three to the power one less than the year.

Step 2 : Trees in year 6

Year 6 : 35 hundred = 243 hundred = 24300

Step 3 : Algebraic expression for year n

Number of trees = 3n−^1 hundred