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.  In answering a homework problem a student found that the population function, P(t), for a population undergoing Logistic growth was given by the formula:                       (20)

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Note that this is not the standard form we have used for such populations but it is a correct formula.

a)  Find .

 

 

 

b) Find the carrying capacity of the population.

 

 

 

 

 

c) Find the initial population, P0.

 

 

 

 

 

d) Find the values of t and P(t) at the inflection point of P(t).

 

 

 

 

 

 

 

2.  Solve for x:   .                                                       (10)

 

 

 

 

 

3.  Find the equation of the line tangent to the graph of  at the point defined by x = 4.                                                                                                         (15)

4.  A radioactive element has a half-life of 12 days.  A shipment arrives at a lab.  20 days after arrival the shipment is opened and it is found that there is 50 grams of the radioactive element left.                                                                                            (16)

a)  How much of the radioactive element was there when it arrived?

 

 

b) Give an expression for M(t), the mass of the radioactive element remaining t days after the shipment arrived.

 

 

 

 

 

 

 

 

 

5.  Evaluate the following limit using L”Hopital’s Rule:  .  Briefly describe your steps and explicitely state when you are using the rule.                  (15)