Respuesta :

tramserran

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]

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