1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly.

a. What will the account be worth in 20 years?

b. What if the deposit were compounded monthly with simple interest?

c. Could you see the situation in a graph?

d. From what point one is better than the other?

2.How do I graph the function f(x)=5(o.5)^{-x} and its reflection across the y-axis on the same axes, and give the x-intercept of the reflection. How do I prove thata^x=e^{x lna}

3.How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed?

The decay equation is A(t)=A_0e^{Kt}, where t is the time for the decay, andKis the characteristic of the material. SupposeTis the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove thatK= \frac{ln0.5}{T}.

What isTfor the uranium-235?