In the andes mountains in peru the number n of species of...

In the Andes mountains in Peru, the number, $N,$ of species of bats is a function of the elevation, $h,$ in feet above sea level, so $N=f(h)$ (a) Interpret the statement $f(500)=100$ in terms of bat species. (b) What are the meanings of the vertical intercept, $k$ and horizontal intercept, $c,$ in Figure $1.9 ?$ (GRAPH CAN'T COPY)

Transcript

00:04 We have this function, n equals f of h.

00:09 N will be the number of bat species in the andes.

00:14 H represents the elevation, how high you are, how many feet you are above sea level.

00:23 So depending on your height above sea level, you can use this function to find the number of bat species that can be expected at that particular elevation.

00:34 At h feet above sea level.

00:38 So f of 500 equals 100.

00:41 F of 500.

00:43 So here, h is 500.

00:46 So that means we are at an elevation of 500 feet above sea level.

00:52 F of h, which is what n equals.

00:55 Okay, this is the number of bat species.

00:59 So in the andes, at an elevation of 500 feet above sea level, c level, you would expect to find 100 different species of bats.

01:12 Now for part b, c is the horizontal intercept.

01:18 At c, at point c, all right.

01:25 So this is a graph of our function, n equals f of h.

01:30 So this is our function, f of h.

01:35 H is the horizontal axis, and then n equals f of h is our vertical axis.

01:48 So at point c, the horizontal intercept, okay, at point c anywhere on this horizontal axis, the function value n is zero.

02:06 So at an elevation of c feet, there will be, because when h, is c okay here's your height when h is c the function value is zero because we're on the horizontal axis think of the y -ac coordinate on the x axis would be zero so when our height is c feet above c level when our elevation is c feet the function is equal to zero well the function is the number of that species that you would expect to find so at an elevation of sea feet above sea level, there will be no bat species.

03:04 There will be zero bat species.

03:15 Now on the vertical axis, on the vertical axis, if this was the x axis and the y axis, on the vertical axis, on the vertical axis, the x coordinate is zero.

03:29 Well, here we don't have the x axis.

03:31 We have the h, okay, the height axis.

03:35 So at this point or at any point on the vertical axis, okay, h is zero.

03:42 So if h is zero, that means we are at sea level...

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