1. An investment of P dollars at interest rate r (in decimal form) compounded annually increases to an amount A = P(1 + r)2 in 2 years. An investment of $5000 increases to an amount greater than $5500 in 2 years. The interest rate must be greater than what percent?
2. A biologist introduces 200 ladybugs into a crop field. The population P of the ladybugs can be approximated by the model P = [1000(1 + 3t)] / (5 + t), where t is the time in days. Find the time required for the population to increase to at least 2000 ladybugs?