To solve this problem, we need to understand that the price of gold increased by the same percentage for two consecutive weeks. This means that we can represent the final price as the initial price multiplied by (1 + percentage increase) twice.

Let's denote the percentage increase as 'p'. Then, the equation we need to solve is:

1024 * (1 + p) * (1 + p) = 2500

First, we need to isolate 'p' in this equation. We can start by dividing both sides of the equation by 1024:

(1 + p) * (1 + p) = 2500 / 1024
(1 + p)² = 2.44140625

Now, we take the square root of both sides to get rid of the square:

1 + p = √2.44140625
1 + p = 1.5625

Subtract 1 from both sides to solve for 'p':

p = 1.5625 - 1
p = 0.5625

To express 'p' as a percentage, we multiply by 100:

p = 0.5625 * 100
p = 56.25%

So, the price of gold increased by 56.25% each week. However, this option is not available in the choices given. There might be a mistake in the problem or the options provided.

Question

To solve this problem, we need to understand that the price of gold increased by the same percentage for two consecutive weeks. This means that we can represent the final price as the initial price multiplied by (1 + percentage increase) twice.

Let's denote the percentage increase as 'p'. Then, the equation we need to solve is:

1024 * (1 + p) * (1 + p) = 2500

First, we need to isolate 'p' in this equation. We can start by dividing both sides of the equation by 1024:

(1 + p) * (1 + p) = 2500 / 1024
(1 + p)² = 2.44140625

Now, we take the square root of both sides to get rid of the square:

1 + p = √2.44140625
1 + p = 1.5625

Subtract 1 from both sides to solve for 'p':

p = 1.5625 - 1
p = 0.5625

To express 'p' as a percentage, we multiply by 100:

p = 0.5625 * 100
p = 56.25%

So, the price of gold increased by 56.25% each week. However, this option is not available in the choices given. There might be a mistake in the problem or the options provided.

Knowee AI · Accepted Answer