Answer:
(3) 48 weeks
Step-by-step explanation:
You want to know the number of weeks it took for revenue to increase from $25000 to $30000 at an annual rate of 21.7%.
Annual compounding
The formula for an amount subject to continuous compounding is ...
A = P(1 +r)^t
where P is the initial amount, r is the annual interest rate, and t is the number of years. We can write this in terms of weeks as ...
A = P(1 +r)^(t/52) . . . . . . where t is in weeks
Time
Solving for t, we get ...
A/P = (1 +r)^(t/52)
log(A/P) = (t/52)log(1 +r)
t = 52·log(A/P)/log(1 +r)
Using the given values, this is ...
t = 52·log(30/25)/log(1.217) ≈ 48.3
She opened the store about 48 weeks ago, choice 3.
