The Strange Tale of the Scholarship and the Beanstalk
Jacqueline, climbing 5 meters each minute, is attempting to reach the top of the beanstalk but at the same time it is also growing at the rate of 2% per minute. Will she ever reach the top and if so when?
This seems to be a new problem for the students, a discrete recursive sequence that includes both additive and multiplicative change.
Imagine our surprise when, upon managing to solve it and feeling quite pleased with ourselves, we discover that this is a familiar problem in disguise, one we recently encountered in the Grade 11 financial math strand!
The scholarship problem. An annual scholarship of $500 is financed by a trust fund with a capital of $7500 growing at an annual rate of 5%. Can the trust fund support the scholarship forever or will it one day run out? In the latter case, for how many years can the scholarships be awarded?