a tennis tournament begins with 64 players. at the end of round one, there will be 32 players. there are 16 players at the end of round 2 and 8 players remaining at the end of round 3. which equation best models this situation?

$y = 64(2)^x$
$y = 0.5x + 64$
$y = 64(0.5)^x$
$y = -32x + 64$

question 17
john invests a sum of money in a retirement account with a fixed annual interest rate of 3.01 % compounded continuously. after 14 years, the balance reaches $48,306.69. what was the amount of the initial investment?

Question

a tennis tournament begins with 64 players. at the end of round one, there will be 32 players. there are 16 players at the end of round 2 and 8 players remaining at the end of round 3. which equation best models this situation?

$y = 64(2)^x$
$y = 0.5x + 64$
$y = 64(0.5)^x$
$y = -32x + 64$

question 17
john invests a sum of money in a retirement account with a fixed annual interest rate of 3.01 % compounded continuously. after 14 years, the balance reaches $48,306.69. what was the amount of the initial investment?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Decay Model", "Continuous Compounding" ], "new_concepts": [], "current_concepts": [ "Exponential Decay Model", "Continuous Compounding", "Present Value" ] } ## Identify the model for the tennis tournament Using the *Exponential Decay Model* knowledge point $$ \begin{aligned} &\text{Initial value } (a) = 64\ &\text{Decay factor } (b) = 0.5\ &y = a \cdot b^x \implies y = 64(0.5)^x \end{aligned} $$ ## Set up the continuous compounding equation Using the *Continuous Compounding* knowledge point $$ \begin{aligned} &A = P e^{rt}\ &A = 48306.69,\quad r = 0.0301,\quad t = 14\ &48306.69 = P e^{0.0301 \times 14} \end{aligned} $$ ## Solve for the initial investment Using the *Present Value* knowledge point $$ \begin{aligned} &P = \frac{48306.69}{e^{0.4214}}\ &e^{0.4214} \approx 1.524097\ &P \approx \frac{48306.69}{1.524097} \approx 31695.29 \end{aligned} $$ ## Question 1 (A) $y = 64(2)^x$

(B) $y = 0.5x + 64$

(C) $y = 64(0.5)^x$

(D) $y = -32x + 64$ ## Question 2 The amount of the initial investment was approximately $\$31,695.29$. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Decay Model" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the model for the tennis tournament

Set up the continuous compounding equation

Solve for the initial investment

Answer:

Question 1

Question 2