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

1 answer

s = k t^ 0.8
64 = k (32)^0.8
k = 64 / 32^0.8
log base 10 of k = 64 - 0.8 log 32
log k = 1.806 - 0.8 * 1.505
log k = 1.806 - 1.204 = .602
so
k = 4
s = 4 t^ 0.8
s = 4 (243)^0.8
= 4 * 81 = 324