Answer:
It will take approximately 1657.3 years.
Step-by-step explanation:
The function that defines the exponential decay for this system is,
[tex]Q(t)=Q_0\cdot e^{-kt}[/tex]
Q(t) = The amount after time t = 20
Q₀ = Initial amount = 24
k = Decay constant = 0.00011
t = time
Putting the values,
[tex]\Rightarrow 20=24\cdot e^{-0.00011t}[/tex]
[tex]\Rightarrow e^{-0.00011t}=\dfrac{20}{24}[/tex]
[tex]\Rightarrow \ln e^{-0.00011t}=\ln \dfrac{20}{24}[/tex]
[tex]\Rightarrow {-0.00011t}\times \ln e=\ln \dfrac{20}{24}[/tex]
[tex]\Rightarrow {-0.00011t}\times 1=\ln \dfrac{20}{24}[/tex]
[tex]\Rightarrow {-0.00011t}=\ln \dfrac{20}{24}[/tex]
[tex]\Rightarrow {-0.00011t}=-0.1823[/tex]
[tex]\Rightarrow 0.00011t=0.1823[/tex]
[tex]\Rightarrow t=\dfrac{0.1823}{0.00011}=1657.3\ years[/tex]
