SOLUTION
We have been given the equation of the decay as
![\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20N%3DN_0e%5E%7B-kt%7D%20%5C%5C%20where%5Ctext%7B%20%7D%20%5C%5C%20N_0%3Dinitial%5Ctext%7B%20amount%20of%20C-14%20at%20time%20t%7D%20%5C%5C%20N%3Damount%5Ctext%7B%20of%20C-14%20at%20time%20t%20%3D%2065%5C%25%20of%20N%7D_0%3D0.65N_0%20%5C%5C%20k%3D0.0001%20%5C%5C%20t%3Dtime%5Ctext%7B%20in%20years%20%3D%20%3F%7D%20%5Cend%7Bgathered%7D)
So we are looking for the time
Plugging the values into the equation, we have
![\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20N%3DN_0e%5E%7B-kt%7D%20%5C%5C%200.65N_0%3DN_0e%5E%7B-0.0001t%7D%20%5C%5C%20e%5E%7B-0.0001t%7D%3D%5Cfrac%7B0.65N_0%7D%7BN_0%7D%20%5C%5C%20e%5E%7B-0.0001t%7D%3D0.65%20%5Cend%7Bgathered%7D)
Taking Ln of both sides, we have
![\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20ln%28e%5E%7B-0.000t%7D%29%3Dln%280.65%29%20%5C%5C%20-0.0001t%3Dln%280.65%29%20%5C%5C%20t%3D%5Cfrac%7Bln%280.65%29%7D%7B-0.0001%7D%20%5C%5C%20t%3D4307.82916%20%5Cend%7Bgathered%7D)
Hence the answer is 4308 to the nearest year
Answer:
677
Step-by-step explanation:
238 + 439 = 677
It is t possible to round it form the ones (dollar) place.
Answer:
is the inequality to find the Domain of f(x)
Step-by-step explanation:
When we have a function where the variable "x" is inside a square root, we find its Domain by looking for all those values x for which the function is defined for the root, which means all the x-values that make the expression inside the root larger than or equal to zero, avoiding the values smaller for which the square root is not defined.
Therefore, in this case , for
![f(x)=\sqrt{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7Bx-3%7D)
we ask for the x-values that verify:
![x-3\geq 0\\x\geq 3](https://tex.z-dn.net/?f=x-3%5Cgeq%200%5C%5Cx%5Cgeq%203)
where we have isolated x on one side of the equal sign.
This would be the definition of the Domain of the function.