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

What will the account be worth in 20 years?

What if the deposit were compounded monthly with simple interest? Could you see the situation in a graph?

From what point one is better than the other?

2.Graph the functionf(x) = 5(0.5)^-xand its reflection about the line y = x on the same axis, and give the x-intercept of the reflection. Prove that a^x= e^xlna. [type y = 5(0.5^-x){- 7 < x < 2}{0 < y < 7} in desmos, and then type its inverse function.]

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

The decay equation isA(t) = Ao e^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 = (ln0.5)/T. What isTfor the uranium -235? Show the steps of your reasoning.