Here’s a question from the May 2023 (US) SAT, non-calculator section:
Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by 10% of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?
I know we can solve this by subtracting 10% of the current value 5 times, but is there a more direct way to solve, maybe as a function?
Yes, an exponential function will work here. The Alice’s first trial is 60 mins, and then each subsequent trial gets shorter by 10%. So you could say that is the number of trials and then say . Note that the is because you don’t want to start subtracting 10% until trial 2–you know trial 1 was 60 minutes, so you want the exponent for trial 1 to be zero.
You can now evaluate for :
All that being said, this being a no-calculator question, most folks will probably find it easier to do the arithmetic one step at a time:
See how I started approximating when the decimals started to grow? Close enough is QUITE good enough for a question like this.