Answer: 2.66 × 10⁻¹³
Step-by-step explanation:
First, use the decay formula [tex]A=A_oe^{kt}[/tex] 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
[tex]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}\\[/tex]
Next, input the k-value and the new t-value to solve for A.
- A = unknown
- A₀ = 300
- k = -0.0240676
- t = 1440
[tex]A=300e^{1440(-.0240676)}\\\\\large\boxed{A=2.66\times 10^{-13}}\\[/tex]
