The time t (in minutes) for a small plane to climb to an altitude of h feet is given by
t = 50 log10 (18000/(18000-h))
where 18000 feet is the plane's absolute ceiling.
a. Determine the domain of the function appropriate for the context of the problem.
b. Graph the function and identify any asymptotes.
c. As the plane approaches its absolute ceiling, what can be said about the time required to further increase its altitude.
d. Find the amount of time it will take for the plane to climb to an altitude of 4000 feet.

Question

The time t (in minutes) for a small plane to climb to an altitude of h feet is given by
t = 50 log10 (18000/(18000-h))
where 18000 feet is the plane's absolute ceiling.
a. Determine the domain of the function appropriate for the context of the problem.
b. Graph the function and identify any asymptotes.
c. As the plane approaches its absolute ceiling, what can be said about the time required to further increase its altitude.
d. Find the amount of time it will take for the plane to climb to an altitude of 4000 feet.

anonymous · Answer

d. 50 log10 (18000/(18000-4000))=5.457

anonymous · Answer

I don't get the rest of the problem.

perl · Answer

a) the domain are the acceptable inputs for the function . here the input of the function is h, or height. you cant have negative height, and there is a 'ceiling' of 18000 for the height . so the domain is

0 <= h <= 18000

perl · Answer

since we are assuming the plane is above ground (negative height implies underground)

perl · Answer

the domain is the set of acceptable inputs for a function, in this case we have an interval for the inputs

anonymous · Answer

Shouldn't it be 0<=h<18000 because it cannot reach the ceiling?