According to the vertex and the directrix of the given parabola, the equation is:
The equation of a quadratic function, of vertex (h,k), is given by:
In which a is the leading coefficient.
The directrix is at y = k + 4a.
In this problem, the vertex is (1,4), hence:
The directrix is at y = 7, hence:
Hence, the equation is:
More can be learned about the equation of a parabola at brainly.com/question/26144898
Answer:
The approximate difference in the half-lives of the isotopes is 66 days.
Step-by-step explanation:
The decay of an isotope is represented by the following differential equation:
Where:
- Current mass of the isotope, measured in kilograms.
- Time, measured in days.
- Time constant, measured in days.
The solution of the differential equation is:
Where is the initial mass of the isotope, measure in kilograms.
Now, the time constant is cleared:
The half-life of a isotope () as a function of time constant is:
The half-life difference between isotope B and isotope A is:
If ,
and
, the difference in the half-lives of the isotopes is:
The approximate difference in the half-lives of the isotopes is 66 days.