MATH 222 Test 1 Part 1 Name________________

Instructions: Answer all the questions on this part. You may not use a calculator on this part. When you are finished, turn in this part and pick up a part 2.

1. Find the derivative of each of the following: (15)

2. Evaluate the following integrals:

MATH 222 Test 1 Part 2 Name________________

Instructions: Answer all the questions on this part. Show all your work. You may use a calculator on all questions.

1. Find the exact value of . (10)

2. Find the area under the graph of from x = 0 to x = ½. (10)

3. Solve for x: (10)

4. A population of frogs is undergoing Logistic growth. The carrying capacity of the environment is 400. The initial population is 50. After one month the population has grown to 70. (20)

a) Find an expression N(t) for the number of frogs at t months.

b) Find .

c) When the population curve (the graph of N(t)) is at its inflection point, how many frogs are there?

d) How many months does it take the population to reach the level of part c?

5. A population of microbes is being grown in a lab. These microbes reproduce at a rate proportional to the population. Starting from an initial population of 12 microbes the population grew to 55 in 3 hours. (25)

a) Find an expression for the number P(t) of microbes at t hours.

b) How many are there after 2 hours?

c) What is the rate of growth of the population at 4 hours?

d) How long does it take the population to double in numbers?

e) How long does it take the population to reach 1000?