The function A=A0e^(-0.0099x) 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. If 600 pounds of the material are initially put into the vault, how many pounds will be left after 90 years?
To find the amount of the radioactive material left after 90 years, we can plug in the value of x = 90 into the given function and calculate.
The given function is A = A0e^(-0.0099x), where A0 is the initial amount of the material in pounds and x is the number of years.
Given: A0 = 600 pounds, x = 90 years, and the function A = A0e^(-0.0099x).
Substituting the values into the function, we get:
A = 600e^(-0.0099 * 90)
To evaluate this expression, we can follow these steps:
1. Multiply -0.0099 by 90: -0.0099 * 90 = -0.891.
2. Substitute the result into the expression: A = 600e^(-0.891).
3. Evaluate e^(-0.891) using a scientific calculator or calculator with an exponent function. The value obtained is approximately 0.4107.
4. Multiply the result from step 3 by 600: A = 0.4107 * 600 = 246.42.
Therefore, after 90 years, there will be approximately 246.42 pounds of the radioactive material left in the concrete vault.