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 $1.10 ?$

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 $1.10 ?$

Key Concepts

Function Evaluation

This concept involves computing or interpreting the output of a function for a given input value. In real-world contexts, such as measuring phenomena or rates, evaluating the function at a specific point helps translate mathematical notation into meaningful information about the situation being modeled.

Vertical Intercept

The vertical intercept is the point where the graph of a function crosses the vertical axis. It represents the value of the function when the input is zero, often providing baseline information or the starting condition of the modeled entity.

Horizontal Intercept

The horizontal intercept is the point where the graph of the function intersects the horizontal axis. This intercept occurs when the output of the function is zero and is used to determine the input value at which the considered quantity reaches zero, marking critical threshold conditions in the model.

Transcript

00:01 So here we have this function given here by this graph where we have n equals f of h, where n is the number of the species of bats, and h is the elevation in feet that we're looking for these bats.

00:13 So we're being asked what a few different things mean.

00:16 The first thing we're being asked about is what it means by f of 500 equals 100.

00:21 So let's take a look at that.

00:22 F of 500 is similar to f of h, where the h is being replaced by 500, which is telling us that our h value is 500.

00:32 When we replace a number with that, we're just saying that that's what it is in this instance.

00:37 So here we're looking at h equals 500, but let's figure out what that is.

00:42 500 what? so since h is the elevation in feet, this is just going to be 500 feet, let's just say above land, when the elevation is 500 feet, in other words.

00:59 And i was look at that 100.

01:01 So the 100 is what f of 500 equals.

01:05 And we know that here it says that n equals f of h, which means f of h is representative of n.

01:11 So f of 500 is the n value at 500.

01:15 So in this case, we're saying the n value is 100, meaning there are 100 species of bats here, because that's what n represents.

01:26 So here we're saying there are...

01:32 100 species of bats.

01:39 Okay, so now we're looking at what k and c represent.

01:43 So k is what value we get when h is zero, because this line right here is our h equals zero line, and that's where k sits.

01:52 So we're looking at that...