In a log-transformed confidence interval for S(t), the endpoints are given by which expression?

• A. (S(t)/Us, S(t)*Us)
• B. (S(t)^(1/Us), S(t)^Us)
• C. (exp(-H(t)/Us), exp(-H(t)*Us))
• D. (S(t) - Us, S(t) + Us)

Answer: (B)

Using a log transformation on S(t) turns multiplicative uncertainty into additive uncertainty on the log scale. When you back-transform, that additive interval becomes a multiplicative, power-based interval for S(t). If the log-scale interval is expressed with a factor Us as the spread, the endpoints on the original scale become exp(ln S(t)/Us) and exp(ln S(t)*Us), which simplify to S(t)^{1/Us} and S(t)^{Us}. This is why the endpoints are powers of S(t). The other forms correspond to additive or different transformations and do not reflect the log-transformed CI for S(t).