<em>✨</em> <em>Using factorisation method</em> <em>✨</em>
Hence , option d is the correct answer
This is a perfect example of exponential decay. In this case the growth factor should be represented by a fraction, and it is! This forest, starting out with apparently ( 800? ) pine trees, has a disease spreading, which kills 1 / 4th of each of the pine trees yearly. Therefore, the pine trees remaining should be 3 / 4.
Respectively 3 / 4 should be the growth factor, starting with 800 pine trees - the start value. This can be represented as such,
- where a = start value, b = growth factor, t = time ( <em>variable quantity</em> )
____
Thus, the function can model this problem. The forest after t years should have P( t ) number of pine trees remaining.
Suppose y= cot x is our parent function then remember general rules of transformation.
1) y= -f(x), reflects the graph of f(x) across x-axis.
2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.
Now, apply these rules to y= -4 cot(x)
the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.
The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.
1. 16
2. 41
3. 367
4. -2
5. 76
6. 58
7. 30
8. 11.25
9. 8
10. 657
11. 492
12. 357