Math half life question please show work thanks alot?

Question

th ebiological half-life of thyroid hormone T4 is about 6.5 days. if a dose of T4 was not followed by repeat doses. how long would it take until only 6.25% of the original does would remain in body? dont u turn the 6.25% into a fraction 25/4 first

Answer 1

Q = q * e ^ ( - 0.6931 * T / t )

Q = final quantity = 0.0625 q

q = initial quantity

e = 2.7183

t = half-life = 6.5 days

T = elapsed time

change the formula around

T = [ - t / 0.6931 ] * Ln (Q / q)

T = [ - 6.5 / 0.6931 ] * Ln (0.0625 * q / q)

T = 26 days