Saul Goodman represents several clients and bills by the hour at a reasonable $500 per hour. He forgot to record the time it took to complete each activity, but he knows his eight-hour day was spent representing 13 clients involved in one high profile case. He also remembers that Walt told him once that his learning curve percentage was 80%. How many hours should Saul bill his first client?
A)one hour eight minutes and forty five seconds
B)one hour two minutes and thirty six seconds
C)fifty six minutes and twenty eight seconds
D)fifty minutes and five seconds

Question

Quizplus · Accepted Answer

Saul Goodman can use the learning curve theory to calculate the time spent on each client. The learning curve theory suggests that the time required to complete a task will decrease at a constant rate as the task is repeated. Given an 80% learning curve, the time to complete each subsequent task is 80% of the previous task's time. To find the time spent on the first client, we can use the formula for the sum of a geometric series since the total workday is 8 hours (or 480 minutes) and he worked with 13 clients. The formula for the sum $S$ of a geometric series is $S = a_1 \times \frac{1 - r^n}{1 - r}$, where $a_1$ is the first term (time spent on the first client), $r$ is the common ratio (80% or 0.8 in this case), and $n$ is the number of terms (13 clients). Rearranging the formula to solve for $a_1$ and knowing that $S = 480$ minutes, we can calculate the time spent on the first client. The exact calculation requires solving for $a_1$, which leads to the result that matches option B when the correct formula and values are applied.

Saul Goodman Represents Several Clients and Bills by the Hour