Complete the following questions utilizing the concepts introduced in this unit.

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 function f(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 that ax=exlna . [Suggestion: type y=5(0.5x) {- 7 < x < 2}{0 < y < 7} in desmos, and then type its inverse function.]

• Link for desmos calculator: https://www.desmos.com/calculator

3.How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed? [See Section 6.6 Example 13].

• Link to this section of the textbook: https://openstax.org/books/algebra-and-trigonometry/pages/6-6-exponential-and-logarithmic-equations

The decay equation is A(t)=A0eKt, where t is the time for the decay, and 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=Tln0.5 . What is T for the uranium-235? Show the steps of your reasoning.