a The time t it takes for sound travel 1 kilometer can be modeled by the following equation.
t=1000/0.6T+331
We will find the air temperature for the given conditions by graphing. To draw a graph on our calculator, we first have to press Y= and write the function on one of the rows. Having written the function, we can press GRAPH to draw it. When we type the equation we should replace T and t with x and y, respectively.
To observe the graph properly, we can set the viewing window as shown below.
Now we press TRACE, and then use the right and left arrow keys to move along the graph to get y≈ 2.9.
The temperature is about 21.3 degrees Celsius.
b To find the average rate of change in time, we will find the ratio of change in time to change in temperature.
r=Change in t/Change in T
By determining t(10) and t(0), we can find the change in time. Let's start!
Temperature, T (^(∘)C)
1000/0.6T+331
Time, t (s
10
1000/0.6(10)+331
2.97
1000/0.6( )+331
3.02
Now, we can find the change in time and temperature.
Change in time:& 2.97-3.02=-0.05
Change in time:& 10- =10
With this information we can find the average rate of change.
r&=-0.05/10
&=-0.005
The average rate of change in time is -0.005 s/ ^(∘)C.
