SOLUTION: Suppose S varies directly as the 2/3 power of T, and that S=16 when T=8. Find S when T= 27

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Question 366005: Suppose S varies directly as the 2/3 power of T, and that S=16 when T=8. Find S when T= 27
Found 2 solutions by amoresroy, Theo:
Answer by amoresroy(361) (Show Source):
You can put this solution on YOUR website!
Suppose S varies directly as the 2/3 power of T, and that S=16 when T=8. Find S when T= 27
Let k = the constant
Equation:
S = k * T^2/3
16 = k * 8^(2/3)
16 = k * (8^1/3)^2
16 = k * (2)^2
16/4= k = 4
When T =27,
S = k * T^2/3
S = k * 27^2/3
= 4 * 3^2
= 36
S = 36 when T = 27

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
S varies directly as the 2/3 power of T.

This means that S = k*T^(2/3)

When S = 16, T = 8

This means that 16 = k*(8^(2/3))

Simplify this to get 16 = k * 4

This makes k = 4

Now that you know the value of k, use the same formula to find S when T = 27.

You get S = k*T(2/3)) which becomes:

S = 4*(27^(2/3)) which becomes:

S = 4*9 which becomes

S = 36