The function A = A0e-0.01386x 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 500 pounds of the material are initially put into the vault, how many pounds will be left after 140 years?

Question

The function A = A0e-0.01386x 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 500 pounds of the material are initially put into the vault, how many pounds will be left after 140 years?

Answer 1

Amount = 500 e^(-.01386(140))

= 71.823

(my keystrokes on my calculators are as follows:
2nd F
ln
(
.01386
±
x
140
)
=
x
500
=

Answer 2

the 500 pounds represent the Ao in the equation (Ao is the initial amount),, since there is time given (x = 140 years), we can substitute the values directly:

A = Ao*e^(-0.01386x)
A = (500)*e^(-0.01386*140)
A = ?
now plug in these values in calculator and you'll get A~

hope this helps~ :)

Answer 3

To find the amount of the radioactive material left after 140 years, we substitute the value of x = 140 into the given equation.

A = A0e^(-0.01386x)

where A0 is the initial amount of material (500 pounds) and x is the number of years (140 years).

So, the equation becomes:

A = 500e^(-0.01386 * 140)

Now we can calculate the value of A:

A = 500e^(-1.9404)

Using a calculator, the approximate value of e^(-1.9404) is 0.1431.

A ≈ 500 * 0.1431

A ≈ 71.55 pounds

Therefore, approximately 71.55 pounds of the radioactive material will be left after 140 years.

Answer 4

To find out how many pounds will be left after 140 years, we can plug in the given values into the equation:

A = A0e^(-0.01386x)

Given:
A0 = 500 pounds (initial amount)
x = 140 years (time)

Now we can calculate the remaining amount, A, by substituting these values into the equation:

A = 500e^(-0.01386 * 140)

To calculate this, we need to find the value of e^(-0.01386 * 140) and then multiply it by 500.

To do this, we can use a scientific calculator or an online calculator.

Using a scientific calculator:
- Enter -0.01386 * 140 and note the result.
- Now find e raised to the power of this result.
- Finally, multiply the result by 500 to obtain the remaining amount in pounds.

Using an online calculator:
Many online scientific calculators have an exponentiation function and the constant "e" built-in. Just enter:
- "-0.01386 * 140" in the exponent field,
- Click on the "e^x" or "exp(x)" button to calculate the exponentiation,
- Multiply the result by 500.

After calculating, you will find the remaining amount in pounds.