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Logarithmic Function

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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 don't 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 don't 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?????

  • Logarithmic Function -

    You continue to approach the station and brake after your sequence begins at 10 km. The craft does not stop until d = 0

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