A major university hires a famous Texas millionaire to manage its endowment. The millionaire decides to follow this plan each year:
• Spend 25% of all funds above $100 million on university operations.
• Invest the remainder at 10% interest.
• Collect $50 million in donations from wealthy alumni.
a. Suppose the endowment has $340 million to start. How much will it have after spending on university operations? After collecting interest on the remainder? After the donations roll in?
b. Find the discrete-time dynamical system.
c. Graph the updating function and cobweb starting from $340 million.