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

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 ( variable quantity )

____

Thus, the function can model this problem. The forest after t years should have P( t ) number of pine trees remaining.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b