Answer:
Part A; Initial dosage is 10 milligrams
Part B:
8.4113 milligrams after 1 hour
5.0057 milligrams after 4 hours.
Step-by-step explanation:
It is given M(h)= 10
Initial dosage is the 10 milligrams
After 1 hour, plug in h as 1
So, M(1)=10
Simplify the right side
M(1)=10(0.84113)
M(1)= 8.4113 milligrams.
Now, after 4 hours
M(4)=10
M(4)=10(0.50057)
M(4) =5.0057 milligrams
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have