M215 Project – Inverse Functions: Domains and Ranges
Section 7.1 - 10 points
Due:
Let a(t) be the altitude in feet of a plane that climbs steadily from takeoff until it reaches its cruising altitude after 30 minutes. We don’t have a formula for a, but extensive research has given us the following table of values:
|
t |
a(t) |
|
0.1 |
50 |
|
0.5 |
150 |
|
1 |
500 |
|
3 |
2000 |
|
7 |
8000 |
|
10 |
12,000 |
|
20 |
21,000 |
|
25 |
27,000 |
|
30 |
29,000 |
1. Is a(t) a one-to-one function? How do you know?
2. What does the
function 
measure in real terms. Your answer
should be descriptive,
similar to the way a(t) was described above.
3. We are interested
in computing values of
. Fill in the
following table for as many
values of x as you can. What quantity does x represent?
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x |
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What are the domain
and range of a? What are the domain and range of ?
4. You are allowed to turn on electronic equipment after the plane has reached 10,000
feet. Approximately when can you expect to turn on your laptop computer after
taking off?
5. Suppose we consider a(t) from the time of takeoff to the time of touchdown.
Is a(t) still one-to-one?