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.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.