Exponential problems

• With calculator: interest rate is r= 6%/yr and compounding period is (a) 1 month, (b) 1 week, (c) 1 day, what is the effective Annual Percentage Rate ?;
• In the compound interest problem, plot A(i T)/A(0) for i=1,...,1/T with T=1, 1/4, 1/12, 1/365 (yr^-1).
• Sketch y = exp(x);
• Use fundamental property of ln to show that exp(a+b)= exp(a) + exp(b).;
• Show that exp(-a)=1/exp(a) ;
• Calculate exp(m) as a function of exp(1) where m is an integer.
• exp(0)=?
• Solve dA/dt= 3A with A(0)=5.
• Solve dA/dt= 7A with A(0)=3.
• Solve dA/dt= 9A with A(0)=0.
• Solve dy/dx=1+y with y(1)=0.