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 was calculated using simple interest?

c.Could you see the situation in a graph?

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

2.Graph the function f(x)= 5(0.5) and its reflection about the line y=x on the same axis, and give the x-intercept of the reflection. Prove that . a = e [Suggestion:y = 5(0.5) {- 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?

I.The decay equation is,A(t)= Ae where t is the time for the decay,

II.K is the characteristic of the material. Suppose T is the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove that. K=ln0.5

T

III.What is Kfor the uranium 235?

IV.Show the steps of your reasoning.