A piece of notebook paper is about 0.0032 inch thick. If you begin with a stack consisting of a single sheet and double the stack 25 times, how tall will the stack be in inches? How tall will it be in feet? (Hint: Write and solve an exponential equation to find the height of the stack in inches. Then use unit analysis to find the height in feet.
a. h = 2^25sheets * 0.0032in/sheet =
107,374.1824 Inches.
b. h = 107,374.1824 / 12 = 8947.85 Feet.
To find the height of the stack in inches, we need to determine how thick the stack will be after doubling it 25 times. The thickness of a single sheet of paper is given as 0.0032 inches.
Let's use an exponential equation to solve for the height of the stack in inches. Each time we double the stack, we are essentially multiplying the thickness by 2. So after doubling it 25 times, we would have:
Height = initial thickness * 2^(number of doublings)
Plugging in the values, we have:
Height = 0.0032 inches * 2^(25 doublings)
To calculate this using a calculator, follow these steps:
1. Take 2 to the power of 25 (2^25) using your calculator. The result will be a very large number.
2. Multiply the large number by the initial thickness of 0.0032 inches.
The resulting number will be the height of the stack in inches.
To convert the height from inches to feet, we can divide the height by 12, as there are 12 inches in a foot. So:
Height in feet = Height in inches / 12
By performing this calculation, we can determine the height of the stack in feet.
Remember to use parentheses or brackets on your calculator to ensure that the calculations are done correctly.