Question

The function a = ape- 001386x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Suppose 400 pounds of the material are initially put into the vault. Answer the following two questions:

Answer 1

The amount of radioactive material remaining can be found using the given function by substituting the number of years since the material was put into the vault. For example, if 5 years have passed, we can find the amount remaining by substituting x = 5 into the function.

Step-by-step explanation:

The given function a = ape-0.001386x represents the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are initially put into the vault, we can substitute this value in the function to find the amount of radioactive material remaining after a certain number of years.

For example, if we wanted to find the amount of material remaining after 5 years, we would substitute x = 5 into the function.

a = 400e-0.001386(5) = 400e-0.00693 ≈ 396.91 pounds.