Question

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

• A. 4 years
• B. 6 years
• C. 8 years
• D. 10 years

Hint:

Separate variables: dA/dt = -k sqrt(A), then use the two data points.

Answer 1

The Correct Option is C

Step 1: Set up with a constant:
$\sqrt A = 100 - mt$ where $m$ is a constant, from $2\sqrt A = -kt + C$.

Step 2: Find m:
$75 = 100 - 2m$ gives $m = 12.5$.

Step 3: Solve for zero:
$100 - 12.5t = 0 \Rightarrow t = 8$. The person is bankrupt after 8 years, option (C).

Final Answer:
The person is bankrupt in 8 years. \[ \boxed{\text{(C) }8\ \text{years}} \]