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An investment lost approximately 5% of the balance each month for the past year. The amount of the investment on January 1^("st ") of last year was $10,000. Which of the following functions, I, models the amount of the investment (in thousands of dollars) at the end of month, n, where 1 <= n <= 12 ? Choose 1 answer: (A) I(n)=10*(1.05)^(n) thousand dollars (B) I(n)=10-0.05 n thousand dollars (c) I(n)=10*(0.95)^(n) thousand dollars (D) I(n)=10+0.95 n thousand dollars

An investment lost approximately 5% 5 \% of the balance each month for the past year. The amount of the investment on January 1st  1^{\text {st }} of last year was $10,000 \$ 10,000 . Which of the following functions, I I , models the amount of the investment (in thousands of dollars) at the end of month, n n , where 1≤n≤12 1 \leq n \leq 12 ?\newlineChoose 11 answer:\newline(A) I(n)=10⋅(1.05)n I(n)=10 \cdot(1.05)^{n} thousand dollars\newline(B) I(n)=10−0.05n I(n)=10-0.05 n thousand dollars\newline(C) I(n)=10⋅(0.95)n I(n)=10 \cdot(0.95)^{n} thousand dollars\newline(D) I(n)=10+0.95n I(n)=10+0.95 n thousand dollars

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Q. An investment lost approximately 5% 5 \% of the balance each month for the past year. The amount of the investment on January 1st  1^{\text {st }} of last year was $10,000 \$ 10,000 . Which of the following functions, I I , models the amount of the investment (in thousands of dollars) at the end of month, n n , where 1≤n≤12 1 \leq n \leq 12 ?\newlineChoose 11 answer:\newline(A) I(n)=10⋅(1.05)n I(n)=10 \cdot(1.05)^{n} thousand dollars\newline(B) I(n)=10−0.05n I(n)=10-0.05 n thousand dollars\newline(C) I(n)=10⋅(0.95)n I(n)=10 \cdot(0.95)^{n} thousand dollars\newline(D) I(n)=10+0.95n I(n)=10+0.95 n thousand dollars
  1. Understand the problem: Understand the problem.\newlineThe investment loses 5%5\% of its balance each month. This means that each month, the investment retains 95%95\% (100%−5%100\% - 5\%) of its value from the previous month. We need to find a function that models this situation over a period of 1212 months.
  2. Analyze the answer choices: Analyze the answer choices.\newlineWe need to find a function that decreases the investment by 5%5\% each month. This means we are looking for an exponential decay function because the investment is losing a constant percentage, not a constant amount.
  3. Evaluate the answer choices: Evaluate the answer choices.\newline(A) I(n)=10×(1.05)nI(n)=10\times(1.05)^{n} thousand dollars - This function suggests the investment is increasing by 5%5\% each month, which is incorrect.\newline(B) I(n)=10−0.05nI(n)=10-0.05n thousand dollars - This function suggests the investment is decreasing by a constant amount each month, which is incorrect.\newline(C) I(n)=10×(0.95)nI(n)=10\times(0.95)^{n} thousand dollars - This function suggests the investment is decreasing by 5%5\% each month, which is correct.\newline(D) I(n)=10+0.95nI(n)=10+0.95n thousand dollars - This function suggests the investment is increasing by a constant amount each month, which is incorrect.
  4. Choose the correct function: Choose the correct function.\newlineThe correct function is the one that models a 5%5\% decrease each month. The only function that represents a 5%5\% decrease each month is option (C) I(n)=10×(0.95)nI(n)=10\times(0.95)^n thousand dollars.

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