Sound travels roughly at 340 m/s. The function d(t)=340t gives the distance d(t), in meters, that sounds travel in t seconds.

Question

A. What isd d(35)? What does this mean in the above context, include units?

B. Would this situation be modeled by a continuous or discrete graph? Explain.

Answer 1

I’m going to translate this equation into words for you first.

distance that sound travels (as a function of time) = 340 times time (and the units will be meters because when you multiply meters per second times the number of seconds you get meters).

When they ask you to find d(35], you need to put 35 seconds into the equation for t and do the arithmetic. When you do that, you will find that you get a distance. In fact it will be the distance that sound travels in 35 seconds.

I know that you can do the arithmetic and I know that you can graph the single point on a piece of graph paper. And then you should be able to figure out part B. :)

Answer 2

A) d(35) means that we are looking for the solution to the function above when t=35, therefore, we are looking for:

1. d(t=35) = 340*(35)

B) To determine whether this function is continuous or discrete, we need to first understand the definition of each term:

1. Discrete graph - a graph of scattered points that do not connect in any way that may not show a trend in anyway. These graphs do not have any data between the points.
2. Continuous graph - a graph that has data between points that can be connected as a continuous line. These graphs are usually created from a function/continuous equation.

In this case, we can see that the function in question can be plotted for any value of t, and a value (output) always exists. this would indicate that this is a continuous function.