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garik1379 [7]
3 years ago
5

A forest has 800800800 pine trees, but a disease is introduced that kills \dfrac{1}{4} 4 1 ​ start fraction, 1, divided by, 4, e

nd fraction of the pine trees in the forest every year. Write a function that gives the number of pine trees remaining P(t)P(t)P, left parenthesis, t, right parenthesis in the forest ttt years after the disease is introduced.
Mathematics
1 answer:
snow_tiger [21]3 years ago
3 0

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,

P( t ) = a( b )^t - where a = start value, b = growth factor, t = time ( <em>variable quantity</em> )

____

Thus, the function P( t ) = 800( \frac{3}{4} )^t can model this problem. The forest after t years should have P( t ) number of pine trees remaining.

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