Stewart_Calc_7ET ch01sec02
MULTIPLE CHOICE
1. Many physical quantities are connected by inverse square laws, that is, by power functions
of the form
.
In particular, the illumination of an object by a light source is inversely proportional to the
square of the distance from the source. Suppose that after dark you are in a room with just
one lamp and you are trying to read a book. The light is too dim and so you move
the distance to the lamp. How much brighter is the light?
a.
times
b.
times
c.
times
d.
times
e.
times
2. Scientists have discovered that a linear relationship exists between the amount of
flobberworm mucus secretions and the air temperature. When the temperature is 65°F, the
flobberworms each secrete 16 grams of mucus a day; when the temperature is 95°F, they
each secrete 22 grams of mucus a day. Find a function M(t) that gives the amount of mucus
secreted on a given day, where t is the temperature of that day in degrees Fahrenheit.
a.
b.
c.
d.
3. The relationship between the Fahrenheit and Celsius temperature scales is given by the
linear function.
9
What is the F-intercept and what does it represent?
a.
, Fahrenheit temperature corresponding to
b.
, Celsius temperature corresponding to
c.
32, Celsius temperature corresponding to
d.
0, Fahrenheit temperature corresponding to
e.
32, Fahrenheit temperature corresponding to
4. The monthly cost of driving a car depends on the number of miles driven. Julia found that in
October it cost her to drive mi and in July it cost her to drive mi.
Express the monthly cost C as a function of the distance driven d assuming that a linear
relationship gives a suitable model.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. It makes sense that the larger the area of a region, the larger the number of species that
inhabit the region. Many ecologists have modeled the species-area relation with a power
function and, in particular, the number of species S of bats living in caves in central Mexico
has been related to the surface area A measured in of the caves by the equation
(a) The cave called mission impossible near puebla, mexico, has suface area of .
How many species of bats would expect to find in that cave?
(b) If you discover that species of bats live in cave estimate the area of the cave.
2. The relationship between the Fahrenheit and Celsius temperature scales is given by the
linear function.
Complete the table and find the slope.