MATH 222 Test 1 - Part I Name____________
Instructions: Answer all the question on the paper provided and show your work. Calculators are not allowed on thisportion of the test.
1. Find the derivative of each of the following functions: (12)
a) 
a)________________
b) 
b)
________________
c) 
c)
________________
2. Evaluate each of the following integrals: (8)
a) 
a)
________________
b) 
b) ________________
MATH 222 Test 1 – Part II Name____________
Instructions: Answer all questions on the paper provided and show all your work. You may use a calculator on all parts of this test.
1. A population
undergoing Logistic population growth has the following population
function: 
where t is measured in
years. (20)
a) What is the carrying capacity of the population?
b) Find 
.
c) Find the initial population, P0.
d) Find the coordinates of the inflection point on the graph of P(t).
2. Find all values of
x such that 
. (8)
3. Find the point of
intersection of the graphs of 
and y = 3. Find the equation of the line tangent to the graph
of at that point. (12)
4. M0 grams of a radioactive element are stored in a nucleur waste facility. Twenty years later it is determined that 70 grams remain. Given that the half life of this element is 85 years find: (20)
a) an expression for M(t), the mass of the element remaining after t years.
b) the amount remaining after 150 years.
5. Find the area of
the region bounded by the x-axis, the lines x = 3, x = 6, and the graph of 
. (15)
6. Solve for x: 
. (5)