Respuesta :
Answer:
[tex]h=40t+9700[/tex]
where the elevation, h, is in feet and time, t, is in minutes.
Step-by-step explanation:
At the time, [tex]t_1=15[/tex] min, the elevation, [tex]h_1= 10,300[/tex] feet and
at the time [tex]t_2= 30[/tex] min, the elevation, [tex]h_2=10,900[/tex] feet.
As they are hiking a steady incline, so the change in the elevation with respect to time will be constant.
So, there will be a linear relationship between the elevation and the time.
Let [tex]h[/tex] be the elevation at any time instant [tex]t[/tex], so the linear relation among these quantities is
[tex]h=mt+C_0\;\cdots(i)[/tex]
where [tex]m[/tex] is the rate of change of elevation with respect to time and [tex]C_0[/tex] is constant.
The change in the elevation, [tex]\Delta h=h_2-h_1= 10,900-10,300=600[/tex] feet.
and the change in time, [tex]\Delta t=t_2-1_1=30-15=15[/tex] min.
So, change in the elevation in unit time,
[tex]m=\frac{\Delat h}{\Delta t}=\frac{600}{15}=40[/tex] feet/min.
Now, from equation (i)
[tex]h=40t+C_0[/tex]
As the elevation, [tex]h=h_1[/tex] at time [tex]t=t_1[/tex], so
[tex]10,300=40\times15+C_0[/tex]
[tex]\Rightarrow C_0=9700[/tex]
Hence, the required equation is
[tex]h=40t+9700[/tex]
where the elevation, [tex]h[/tex], is in feet and time, [tex]t[/tex], is in minutes.
