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1. The conoept of compound interest is based on the idea that the amount of interest accrued in a given amount of time is proportional to the amount of money invested or borrowed. The more you invest, the more you earn. Assume a principal amount of money P i; invested and is earning interest at interest rate r compounded continuously. a] Express the growth rate ofthe investment using a dilferential equation. b] Solve this diiferential equation to derive the formula for oontinuousl'yr compounded interest. 2. A learning curve is the graph of a function P[t), where P represents the performanoe of a learner as a function of the training time t. a] Based on what you understand about learning, explain what happens to (fth {the rate at which performance improves] as t increases, and explain why you think this. b] Let M represent the maximum level of performance of which the learner is capable. Explain why the diiferential equation below is a reasonable model for learning. {IFMM P) can dr c] Draw the graph of a possible solution of this differential equation