Question

The initial rate of appreciation of a collectible toy may be modeled by the equation
50
=
10
e
3
k
, where 50 represents the current value and 3 represents the number of weeks that have passed. Which of these best represents the rate of appreciation, k?

Answer 1

Start with 50 = 10 e^{3k}. Divide by 10: 5 = e^{3k}. Take natural log: ln 5 = 3k, so

k = (ln 5)/3 ≈ 1.60944/3 ≈ 0.5365 (per week).