Jacqueline and the Beanstalk

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?

Teacher manual
Student workbook