MATHEMATICS 184 (Section 921) - TERM EXAM 1
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INSTRUCTIONS: Notes, books and calculators are not permitted.
Answers may receive no credit if accompanying work is not provided. Simplify all answers as much as possible, and be sure to
clearly indicate the final answer for each question. Please use the
back of the pages if you need extra space.
1. Two populations of bacteria are raised in a laboratory for an
experiment. Colony A is provided with a limitless supply of food,
and so is found to double in size each day. Colony B is not provided
with any food and so is found to decrease each day to 1/3 of the
previous day’s size.
(a) If the initial population size of bacteria colony B is PB , write
an expression for the number of bacteria in colony B after t days.
[2]
(b) At this rate of decrease, how long will it take for bacteria colony
B to be reduced to 20% of its original size?
[4]
(c) If there were initially ten times more bacteria in colony B than
in colony A, after how many days would there be the same number
of bacteria in both colonies?
[6]
2. (a) John Dough has purchased a guaranteed investment certificate (GIC) that pays 4.5% nominal interest compounded annually
for the first year, followed by 5% nominal interest compounded
monthly for all subsequent years. If he initially invested 1 million
dollars, how much would Mr. Dough’s investment be worth after
5 years? (You may express your answer in millions of dollars)
[7]
(b) What would John Dough’s investment be worth after the same
5 years if instead he had invested his million dollars at a competing
bank that offered 4% compounded continuously?
[4]
3. Suppose that a ball is dropped from the upper observation
deck of the CN tower, 490m above the ground. The height, h (in
meters), of the ball above the ground after t seconds is given by
the equation h = 490 − 4.9t2 .
(a) What is the average velocity of the ball during its descent to
the ground?
[6]
(b) How fast is the ball travelling at the moment it hits the ground?
[6]
4. Let
f (x) =
√
2x − 1
(a) What is the value of f 0 (3)?
[6]
(b) Find an equation for the straight line that passes through the
point (3, f (3)) and that has slope f 0 (3) (from part (a)).
[4]