Answer:
10.8 g
Step-by-step explanation:
Exponential decay equation: [tex]A=A_0e^{-rt}[/tex]
[tex]A_0[/tex] is the initial amount (at time t = 0, "noon")
r is the decay rate
You have two pieces of information:
Noon t = 0 [tex]A_0=50[/tex]
3:00 pm t = 3 [tex]A=30[/tex]
Plug those in to get [tex]30=50e^{-r(3)}[/tex]
Divide by 50.
[tex]0.6=e^{-3r}[/tex]
Take the natural log of both sides.
[tex]\ln(0.6)=-3r[/tex]
Divide by -3.
[tex]\frac{\ln{(0.6)}}{-3}=r\\\\r \approx .17027[/tex]
Now, for 9:00 pm, use this value of r and t = 9.
[tex]A=50e^{-.17027(9)} \approx 10.8[/tex]
