The decay constant for americium 241 is . If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years?
The amount of americium 241 present in 500 years will be approximately
(Round to the nearest whole number.)

Question

The decay constant for americium 241 is

. If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years?
The amount of americium 241 present in 500 years will be approximately
(Round to the nearest whole number.)

UpStudy AI · Accepted Answer

Given:
- Decay constant for americium 241, $$ k = -0.002108 $$
- Initial amount of americium 241, $$ N_0 = 5 \, \text{mg} $$
- Time period, $$ t = 500 \, \text{years} $$

We can use the exponential decay formula to find the amount of americium 241 present after 500 years:
$$ N = N_0 \times e^{kt} $$

Substitute the given values into the formula:
$$ N = 5 \times e^{-0.002108 \times 500} $$

Now, we can calculate the amount of americium 241 present after 500 years.
Calculate the value by following steps:
- step0: Calculate:
  $$5e^{-0.002108\times 500}$$
- step1: Multiply the numbers:
  $$5e^{-1.054}$$
- step2: Convert the expressions:
  $$5e^{-\frac{527}{500}}$$
- step3: Evaluate the power:
  $$5\times \frac{e^{\frac{473}{500}}}{e^{2}}$$
- step4: Multiply:
  $$\frac{5e^{\frac{473}{500}}}{e^{2}}$$
- step5: Simplify:
  $$\frac{5\sqrt[500]{e^{473}}}{e^{2}}$$
The amount of americium 241 present after 500 years will be approximately 1.742704 milligrams. Rounding to the nearest whole number, the amount will be 2 milligrams.
The amount of americium 241 present after 500 years will be approximately 2 milligrams.

The decay constant for americium 241 is . If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years?
The amount of americium 241 present in 500 years will be approximately
(Round to the nearest whole number.)

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The decay constant for americium 241 is . If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years? The amount of americium 241 present in 500 years will be approximately (Round to the nearest whole number.)

Upstudy AI Solution

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Solution

The Deep Dive

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Latest Pre Calculus Questions

The decay constant for americium 241 is . If 5 milligrams ( mg ) of americium 241 is sealed in a laboratory container today, how much will be present in 500 years?
The amount of americium 241 present in 500 years will be approximately
(Round to the nearest whole number.)