Suppose that a savings account is opened with an initial deposit of $2000. Also, the account earns an interest that is compounded each month at an interest rate that keeps increasing each month: 0.10%, 0.11%, 0.12%, 0.13%, 0.14%, 0.15%,... For each of the deposit scenarios (a), (b), (c) described below, construct a discrete dynamical system for the account balance each month by writing a single, linear, non-autonomous equation for Pn+1in terms of Pn.
(a) $100 is deposited at the end of every month.
(b) The amounts deposited at the end of subsequent months are: $100, $50, $100, $50, $100,...
(c) The amounts deposited at the end of subsequent months are: $100, $150, $175, $187.50, $193.75