Question

of an initial amount of 2000 g of lead - 210, how much will remain in 130 years? lead - 210 decays at a rate of 3.15%/yr.
(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, and $t$ is the time.

Step2: Substitute the given values

Here, $A_0=2000$, $r = 0.0315$ (since $3.15\%=0.0315$), and $t = 130$. So, $A=2000\times(1 - 0.0315)^{130}$.

Step3: Calculate the value

First, calculate $(1 - 0.0315)=0.9685$. Then, find $(0.9685)^{130}$. Using a calculator, $(0.9685)^{130}\approx0.01777$. Multiply by $2000$: $A = 2000\times0.01777 = 35.54$.

Step4: Round the result

Rounding to one - decimal place, we get $A\approx35.5$.

Answer:

$35.5$