math
posted by red .
A manatee swimming 3 feet below the water surface, ascends 2 feet, descends another 5 feet then ascends another 2 feet. Write an expression to find his position relative to the water surface. Then find His position

math 
red
please help me with this

math 
Ms. Sue
3 + 2  5 + 2 = ?

math 
MathMate
The expression is a step function, which has discontinuities between ascents and descents.
Let the number of movements (ascents or descents) be i, and
h(i) = position relative to the surface after the ith movement.
h(0)=3 (3 feet below surface)
h(1)=1 (=3+2)
h(2)=6 (=15)
h(3)=4
h(4)=9
h(5)=7
...
So
h(i) = (i/2)*3 3 for 2i (i divisible by 2), and
h(i) = (i+1)/2*3 +2
= (3i1)/2 for 2(i+1) (i not divisible by 2) 
math 
MathMate
Ms Sue, you're right. An expression can be all numeric!
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