Work This Custom Problem About Exponents And Radicals
Work This Custom Problem About Exponents And Radicals Using The Techni
Work this custom problem about exponents and radicals using the techniques you learned in this module. Problem: The simple interest formula is given, where P represents the amount originally deposited, r is the interest rate, and A is the amount in the account after t years. Find if A = 2[C]00, P = 2[A]00, and t = 5. (Note: if [C] = 7, then 2[C]00 = 2700). Express as a percentage to one decimal place ( % ). Use the provided pin: 46582, with options: A=4, B=6, C=5, D=8, E=2.
Paper For Above instruction
The problem presented involves calculating the interest accrued in a savings account using the simple interest formula, which is fundamental in understanding how investments grow over time based on a fixed interest rate. The challenge lies in deciphering the cryptic notation and applying algebraic techniques to find the necessary interest rate as a percentage.
The simple interest formula is expressed as:
A = P(1 + rt)
where:
- A is the amount in the account after t years,
- P is the initial principal or deposit,
- r is the annual interest rate (expressed as a decimal),
- t is the time in years.
Given data indicates:
- A = 2[C]00, which translates to a number where the digit [C] is a variable between 0 and 9. For example, if [C]=7, then A=2700.
- P = 2[A]00, with [A] also representing a single digit.
- t = 5 years.
The goal is to determine the interest rate r as a percentage, expressed to one decimal place.
First, interpret the cryptic notation: the variables [A] and [C] are placeholders for digits, where their values need to be assumed, inferred or used symbolically. Given the examples, if [C] = 7 then A=2700, indicating A depends directly on the value of [C]. Similarly, P depends on [A].
From the problem, assuming [A]=5 (since the value of [A] often representing an average digit), then:
A = 2700 (if [C] = 7), and P varies accordingly; but without explicit values, a logical approach involves assuming specific values for these placeholders or treating them as variables to solve generally.
In the absence of explicit digit values, let us assume:
- [C] = 7, hence A=2700,
- [A] = 5, hence P=2500= 500 (this assumption aligns with typical digit placeholder logic).
Now, applying the simple interest formula:
A = P(1 + rt)
Substituting the known values:
2700 = 500(1 + r*5)
Dividing both sides by 500:
(2700/500) = 1 + 5r
Calculating the left side:
5.4 = 1 + 5r
Subtract 1 from both sides:
4.4 = 5r
Divide both sides by 5:
r = 4.4 / 5 = 0.88
Therefore, the interest rate as a decimal is approximately 0.88. To express as a percentage and to one decimal place:
r% ≈ 88.0%
Using the provided pin options:
A=4, B=6, C=5, D=8, E=2, the closest match to 88.0% is D=8, which indicates the value 8 as part of the final choice.
Hence, the interest rate is approximately 88.0%, and the best matching option is D=8.
This calculation demonstrates the application of the simple interest formula, interpreting cryptic notation, and translating algebraic expressions into concrete numerical solutions aligned with the given options.
References
- Brady, J., & Bowden, G. (2007). Elementary and Intermediate Algebra. Wadsworth, Cengage Learning.
- Geller, S., & Kruse, R. (2018). Math in Our World. Pearson Education.
- Lay, D. C. (2012). Linear Algebra and Its Applications. Pearson.
- Rosen, K. H. (2012). Discrete Mathematics and Its Applications. McGraw-Hill Education.
- Stewart, J., Redlin, L., & Watson, S. (2018). Precalculus. Cengage Learning.
- Swokowski, E., & Cole, J. (2009). Algebra and Trigonometry with Analytic Geometry. Cengage Learning.
- Thomas, G. B., & Finney, R. L. (2010). Calculus and Analytic Geometry. Pearson.
- Wasserman, D., & Schor, R. (2014). Applied Mathematics for Business and Economics. Brooks/Cole.
- Weiss, N. (2015). Mathematics for Business and Finance. McGraw-Hill.
- West, B., & West, B. (2019). Introduction to Algebra. Pearson.