Answer: A = P * e^(-k*t)
Step-by-step explanation:
To calculate the amount of waste remaining (A) in tons, t years after 1970, you can use the following formula:
Where:
- A represents the amount of waste remaining in tons
- P represents the initial amount of waste in tons (at t = 0)
- e is Euler's number, approximately equal to 2.71828
- k is the decay constant (a positive value)
Here's a step-by-step explanation of how to use the formula:
1. Determine the initial amount of waste, P, in tons at t = 0. This is the starting point for your calculation.
2. Determine the decay constant, k, which represents the rate at which the waste decays over time. The specific value of k depends on the type of waste and its decay characteristics. It can be determined through experimental data or provided in the problem statement.
3. Determine the number of years, t, since 1970. This is the time period for which you want to calculate the remaining waste.
4. Plug in the values of P, k, and t into the formula A = P * e^(-k*t).
5. Calculate the exponent term, -k*t.
6. Raise Euler's number, e, to the power of the exponent calculated in the previous step.
7. Multiply the result of step 6 by the initial amount of waste, P, to get the amount of waste remaining, A, in tons.
It's important to note that the specific values of P and k will vary depending on the problem or scenario. Additionally, the formula assumes that the decay of waste is exponential, which may not always be the case in real-world situations.