Question

Suppose that S varies directly as the 4/5 power of T, and that S=64 when T=32. Find S when T=243

Answer 1

\[32=2^{5}\]
So substituting the above value for 32 we get
\[64=k \times (2^{5})^{\frac{4}{5}}=k \times 2^{4}.......(1)\]
Now you can solve equation (1) to find the value of k, the constant of proportionality.

Also
\[243=3^{5}\]
Therefore
\[S=k \times (3^{5})^{\frac{4}{5}}=k \times 3^{4}..........(2)\]
The solution can be found by plugging the value for k into equation (2)