# Thread: Log word problem #2

1. ## Log word problem #2

A spacecraft is approaching a space station that is orbiting Earth. When the craft is 1000 km from the space station, reverse thrusters must be applied to begin braking. The time, t, in hours, required to reach a distance, d, in km, from the space station while the thrusters are being fired can be modelled by t=log_0.5(d/1000). The docking sequence can be initalized once the craft is within 10 km of the station's docking bay.

a) how long after the reverse thrusters are first fired should docking procedures begin.

I dont need help with this one.

b) What are the domain and range of this function and what do these represent?

I need help with this.
I am not sure if my graph of this function looks right because I dont have graphing software or a calculator. If someone could show me a picture of it that, I would appreciate it. But otherwise, could you just explain to me why the domain and range are what they are.

The domain is supposed to be 0<d< or = 1000
but why isn't it 10<d< or = 1000
Doesnt it say in the question that "the docking sequence can be initialized once the craft is within 10 km of the station's docking bay", hence the 10 and not 0 in the domain?????

If someone could just clarify the domain for me, that would be helpful. thank you!!

2. The domain is supposed to be 0<d< or = 1000
but why isn't it 10<d< or = 1000
Doesnt it say in the question that "the docking sequence can be initialized once the craft is within 10 km of the station's docking bay", hence the 10 and not 0 in the domain?????
The docking sequence can start when the craft is within 10km, but that fact isn't related to the function at all. The function just tells how long it takes for the space craft to be a certain distance from the space station. The domain is then 0<d<= 1000 because the function begins to work when the space craft is 1000km away, and it obviously stops working when the distance between the spacecraft and station is 0m.

Or think of it like this: the spacecraft is still moving toward the space station while it is docking. The spacecraft only stops when it hits the space station (0 km away).