Exponential Logarithmic Transformations Worksheets Grade 12

1. A solid is formed by rotating the region bounded by the curve y = e^x, the x-axis, the y-axis, and the vertical line x = 2 about the x-axis. Using the method of disks, determine the volume of this solid of revolution.
2. A solid is formed by rotating the region bounded by the curve y = e^x, the x-axis, and the vertical lines x = 0 and x = 2 about the x-axis. Using the method of disks, determine the volume of this three-dimensional shape.
3. log₂(16) + ln(e⁴) = ?

…and 5 more problems

1. A pharmaceutical company is modeling the concentration of a new medication in a patient's bloodstream over time. The concentration C(t) in milligrams per liter is given by C(t) = 80e^(-0.15t) - 20e^(-0.08t), where t is time in hours. Determine the time when the medication concentration reaches its maximum level, and find that maximum concentration.
2. A solid is formed by rotating the region bounded by the curve y = ln(x), the x-axis, and the vertical lines x = 1 and x = 4 about the x-axis. Using the method of disks, determine the volume of this three-dimensional solid. (Express your answer in terms of π.)
3. A geometric solid is formed by rotating the region bounded by the curve y = e^x, the x-axis, and the vertical lines x = 0 and x = 2 about the x-axis. This creates a 3D volume. What is the volume of this solid? (Use π in your answer)

…and 5 more problems

1. A solid is formed by rotating the region bounded by the curve y = e^x, the x-axis, the y-axis, and the vertical line x = 2 about the x-axis. Describe the resulting 3D shape and find its volume using integration.
2. A geometric solid is formed by rotating the region bounded by the curve y = ln(x), the x-axis, and the vertical lines x = 1 and x = 4 about the x-axis. Using the method of disks, determine the volume of this three-dimensional solid. (Express your answer in terms of π.)
3. log₂(8) + ln(e³) = ?

…and 5 more problems