Calculus I
Quiz 1
EFTP – Summer B, 2008
Name:
Calculus I Quiz I
EFTP – Summer B, 2008
July 8, 2008
General:
This quiz consists of 3 free response questions. For optimum optimal credit show as much work
as you can without being excessive.
Directions:
Please clear your desk of everything except for pencils and pens. The exam is closed book and
you are not allowed calculators or formula sheets. Leave substantial space between you and your
neighbor. Show your work on the space provided on the exam. I can provide additional scratch
paper if needed.
Fill in your name at the top of this page and sign the Honor Code statement below.
The Honor Code:
On my honor, I have neither given nor received unauthorized aid in doing this assignment.
Signature
1 of 1
Question 1. Work each of the following and SHOW YOUR WORK:
(a) Find the exact value of:
log4
1
64
(b) Simplify the expression using trig identities or triangles:
tan(sin−1 x)
(c) Find the exact value of:
log10
√
10
Question 2. The average height of the ocean tide in Istanbul, Turkey
is 30cm and the magnitude varies from maximum to minimum
by ±5cm. The maximum tide occurs every 12 hours.
(a) Model the magnitude of the tide variations as a function of time in hours. Sketch the function. Don’t forget to label your axes and units.
(b) Using the function you found in part (a), how would
you shift the function to model the tide variations in
Marseille, France if the maximum tide occurs 2 hours
later? Show the new equation.
Question 3. When a camera flash goes off, the batteries immediately
begin to recharge the flash’s capacitor, which stores electric charge
given by
t
Q(t) = Q0 (1 − e− a )
(The maximum charge capacity is Q0 and t is measured in seconds.)
(a) Find the inverse of this function and explain its meaning.
(b) How long does it take to recharge the capacitor to 90%
of capacity if a = 2?