Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina

Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina - 2013 Page 2

BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA

4 (3 Points). (a) State the general form of an exponential function.

(b) When does such a function model exponential growth?

Solution. (a) The general form of an exponential function is

f (t) = Ca .

(b) The function f models exponential growth when a > 1.

5 (2 Points). Consider the two lines f (x) = m

x + b

an g(x) = m

x + b

(a) When are f and g parallell

(b) When are f and g perpendicular?

Solution. (a) The lines f and g are parallel whenever m

= m

(b) The lines f and g are perpendicular whenever any of the following three equivalent

conditions hold,

(i) m

(ii) m

, or

(iii) m

6 (16 Points). In the following problems, use the given information to ﬁnd the equation of

the line in slope-intercept form.

(a) The line passing through the points (2, 5) and (4, 13).

(b) The line passing through the point ( 3, 3) and parallel to the line 2y

4x = 20.

line 2y

4x = 20.

Solution. (a) First we calculate the slope of the line, m,

m =

= 4 or m =

= 4.

Then we can form either of two lines in Point-Slope form,

13 = 4(x

4) or y

5 = 4(x

2).

For the ﬁrst one, we can put it into Slope-Intercept form by distributing on the right-hand

side and adding 13 to both sides, which gives

y = 4x

16 + 13 = 4x

Math 111: Exam 02 Solutions - Blake Farman - University Of South Carolina - 2013 Page 2