There you go! Hope this helps
Answer:B
Step-by-step explanation: dy/dx = (1--4)/(-10-0)
= 5/-10
=-1/2
The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.
To solve this question we will use two important formulas.
The first formula involves the calculation of the decay constant, 
which is to be found as:
where 
is the half life of Pb-210 which is given to be 22 years in the question.
Thus, 
Now, we will use the second formula which is called the function of decay formula and is given as:
where 
percentage of Pb-210 remaining in the bone at present, which in our case is 67% or 0.67
percentage of Pb-210 to start with, which is always 100% or 1.
Plugging in all these values in the decay formula we are supposed to find the time, 
.
Taking natural log on both sides we get:
years
Therefore the bone fragment is about 12.71 years old.
