# Math 0914 Exam 2

**Directions:** You have **90 minutes** to answer
the following questions. **You must show
all your work **as neatly and clearly as possible and indicate the final
answer clearly. You

may use only a TI-30 calculator. The last page contains formulas that you might find

useful. You may tear that page out.

If you are feeling ill you should inform the proctor. The proctor will note your name and

Poly ID, and will accept any written statement(s) that you may wish to make regarding

your illness.

Problem | Possible | Points |

Total | 100 |

(1) (Page 89, Problems 18, 21) A ball is thrown upward.
Its height (expressed in feet)

t seconds later is given by

h(t) = 96t - 16t^{2}.

Show all your work, and include units in your answers.

(a) Evaluate and interpret h(4).

(b) Solve and interpret the equation h(t) = 96.

(c) When does the ball hit the ground?

(2) (Page 88, Problems 9-15) Find the quadratic function
whose roots are -1 and 2,

y-intercept is 2. Show all your work.

(3) (Page 99, Problems 113-120) Consider the following
system of equations

(a) Solve the system of equations for x and y. Show all your work.

(b) Graph the functions and show the solutions on the plane.

(4) (Page 109, Problem 25) At time t hours after taking
antibiotic ampicillin the

amount, A, in grams, remaining in the body is given by

A = 2.5 (0.84)^{t} .

Fill in the blanks. You do not have to explain, but you must include units in
your

answers.

(a) The initial dose of ampicillin is .

(b) The percentage of ampicillin that leaves the body each hour is
.

(c) The amount of ampicillin left in the body 5 hours after the injection is
.

(d) The time it takes until only 1.25 g of ampicillin remains in the body is
.

(5) (Page 117, Problems 9-14) Find a possible formula for
the graph of the following

exponential function. Show all your work.

(6) (Page 134, Problems 29, 30) Determine which of the
functions given in the table be-

low is linear and which is exponential. Write formulas for the linear and
exponential

functions. Show all your work.

The linear function is , and its formula is
.

The exponential function is , and its formula is
.

(7) (Page 123, Problems 11-14, 20) Three exponential
functions are graphed in a figure

below. Six constants a, b, c, d, p and q determine these functions.

Answer the following questions. You do not have to
explain.

(a) Which of the constants are positive?

(b) Which of the constants are definitely between 0 and 1?

(c) Which of the constants are definitely greater than l?

(d) Which of the two constants are definitely equal?

(e) Which of the two constants COULD be equal?

a and p,

q and d.

(8) (Page 137, Problem 14-30) Determine weather each of
the following statements is

True or False. You do not have to explain.

(a) If a population increased by 50% each year, then in two years it increases
by

100%.

(b) If a > 1 in the formula Q = ab^{t}, then the graph always rises as we read from

left to right.

(c) In the formula Q = ab^{t}, the value a tells you where the graph crosses the

Q-axis.

(d) If P = 10e^{0.2t} , we say the continuous growth rate of the function is 2%.

(e) Investing $1,000 for 30 years at 4% earns more if interest is compounded

monthly than if it is compounded annually.

(9) (Page 130, Problems 4-6) A population grows from its
initial level of 25,000 at a

continuous rate of 7.4% per year.

(a) Find a formula for P(t) the population in year t. Show all your work.

(b) By what percent does the population increase each year? Show all your work.

(10) (Page 142, Problem 104) Let h(t) = 1 + b^{t}. Show that

**Useful formulas**

• Factored form of a quadratic function:

• Vertex form of a quadratic function:

y = a(x - h)^{2} + k