MATH-Written Assignment Unit 5
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School
Northern Virginia Community College *
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Course
1280
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
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2
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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?
The compound interest formula is A = P(1 + r/n)^nt A = final amount P = initial principal balance r = interest rate n = number of times interest applied per time period t = number of time periods elapsed” (Google, 2021) Using this information, we can substitute the letter values for their numeric values. Doing this leaves us with the equation:
A = 8,500(1 + 0.0812/12)^(12)(20).
Solving this equation:
A = 8,500* (1.0068)^240
A = 8,500*5.08592147259
A = 43,230.332517
Could you see the situation in a graph?
To do this we first need to convert the equations into graph-able formulas.
A(t) = 8500(1.0068)^12t
A = 8500(1 + 0.0812t)
2. Graph the function
and its reflection about the line y=x on the same axis, and give the x-intercept of the reflection. Prove that
. [Suggestion: type
{- 7 < x < 2} {0 < y < 7} in desmos, and then type its inverse function.]
Doing this means the inverse of the above f(x) function comes to:
F^-1 (x) = -In (x/5) / In (0.5)
Now I can graph both the function and its inverse with Desmos. The two functions, as seen in the
graph, are reflections of each other. They are not, however, reflected over the symmetry line. This, I believe, is due to the domain and range I used.
The reflection's x-intercept is: (5,0)
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]
The decay equation is
, 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
. What is K for the uranium-235? Show the steps of your reasoning.
226 years, 572 years, 993 years
Demonstrate that K=fracln0.5T.
To demonstrate this, I'll simply answer the original equation for K. As a result, K = In0.5/T will be established.
See what I've come up with below:
What is the K value for uranium-235? Demonstrate how you arrived at your conclusions.
K = -109 is the answer to this.
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