Question

of an initial amount of 5000 g of lead - 210, how much will remain in 190 years? lead - 210 decays at a rate of 3.15%/yr.

□ g
(round to one decimal place as needed.)

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay per - year, and $t$ is the number of years.

Step2: Substitute the given values

Here, $A_0=5000$ g, $r = 0.0315$ (since $3.15\%=0.0315$), and $t = 190$ years. So, $A=5000\times(1 - 0.0315)^{190}$.

Step3: Calculate the value

First, calculate $1-0.0315 = 0.9685$. Then, find $(0.9685)^{190}$. Using a calculator, $(0.9685)^{190}\approx0.00227$. Multiply by $A_0$: $A = 5000\times0.00227 = 11.35$.

Answer:

$11.4$ g