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 was calculated using 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(o.5)^-x and its reflection about the line y=x on the same axis, and give the x-intercept of the reflection. Prove thata^x =e^xlna.. [Suggestion: typey= 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 is A(t) = A_o^eKt , 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 that. What isKfor the uranium-235?