145 hours.
Explanation: Riding a bicycle for one hour expends 505 kcal of energy. Given that one gram of body fat equals 7.70 kcal, and 1 pound of body fat is equivalent to 454 grams:
1 lb = 454 g; thus, 21 lb = 21 × 454/1 = 9534 g. Moreover, converting 9534 g of body fat gives us 9534 × 7.70 kcal/1 = 73411.8 kcal. If riding for one hour burns 505 kcal, then to lose 73411.8 kcal, it would require 73411.8 kcal x 1 hour/505 kcal = 145 hours.
An exponential decay law is generally expressed as: A = Ao * e ^ (-kt) => A/Ao = e^(-kt) Half-life time => A/Ao = 1/2, and t = 4.5 min => 1/2 = e^(-k*4.5) => ln(2) = 4.5k => k = ln(2) / 4.5 ≈ 0.154. Now substituting k, Ao = 28g, and t = 7 min to determine the remaining grams of Thallium-207 gives: A = Ao e ^ (-kt) = 28 g * e ^( -0.154 * 7) = 9.5 g. Final answer is 9.5 g.
