Question

Strontium-90 has a half-life of 28.8 years. If you start with a 300-gram sample of strontium-90,

Answer 1

Answer:  2.66 × 10⁻¹³

Step-by-step explanation:

First, use the decay formula   $A=A_oe^{kt}$   where

• A is the final amount (amount left)
• A₀ is the initial amount (amount you started with)
• k is the rate of decay (you need to solve for this)
• t is the time

Given:

• A = 1/2(300) = 150
• A₀ = 300
• k = unknown
• t = 28.8

$150=300e^{28.8k}\\\\0.5=e^{28.8k}\\\\ln(0.5)=ln(e^{28.8k})\\\\ln(0.5)=28.8k\\\\\\\dfrac{ln(0.5)}{28.8}=k\\\\\\\large\boxed{-0.0240676=k}$

Next, input the k-value and the new t-value to solve for A.

• A = unknown
• A₀ = 300
• k = -0.0240676
• t = 1440

$A=300e^{1440(-.0240676)}\\\\\large\boxed{A=2.66\times 10^{-13}}$