Section 1.1
2.
4.
8.
92.138 203 Calculus for the Life Sciences I
y = 3.5 (see graph).
y
4
Solutions
y = 3x
x = 10
2
x = 10 (see graph).
.
2
Slope m = 3 (see graph).
x
2
4
6
10
y = 3x + 2
2
4
12. Slope m = 3 (see graph).
8
y = 3.5
14. Solve for y: y = 2x +
Section 3.1
4.
92.138 203 Calculus for the Life Sciences I
Solutions
f (x) = 3 4x = 0 when x = 3/4 and the sign of f is
+
.
x
3/4
y
2
so (3/4, 25/8) is a maximum; or . . .
3
2
.
1
Its a downward facing parabola so has a maximum at the vertex
1
x
2
(3/4, 2
Quiz Solutions
92.138 203 Calculus for the Life Sciences I
Spring 2014
1. (1 / 28) Find the slope and slope-intercept equation of the line through
the points (1, 3) and (2, 9).
The slope is
39
1 (2)
=
6
3
y
9
= 2 so the point-slope equation of the
6
line
Section 2.3
92.138 203 Calculus for the Life Sciences I
Solutions
21 8
1.4 pounds/month.
9
17 8
(b) Average rate of growth in rst 6 months
1.5 pounds/month.
6
13 8
(c) Average rate of growth in rst 3 months
1.7 pounds/month.
3
14. (a) Average rate of
Section 4.1
92.138 203 Calculus for the Life Sciences I
2.
Solutions
y
5
4
3
2
1
2
.
1
x
1
t
1
2
5
N
8.
52.50
55.13
63.81
N (t) = N0 (1 + r)t = 50(1.05)t
14. f (x) = 12e3x .
22. f (x) = 5x4 ex + x5 ex = (x + 5)x4 ex .
40. y = sin x ecos x .
54. y =
ex (1
Exam 1 Solutions
92.138 203 Calculus for the Life Sciences I
Spring 2014
1. (a) Find the amplitude, period and midline of 2 cos 2t + 3.
Amplitude = 2
Period = 2/2 =
Midline = 3.
(b) Sketch the graph of y = 2 cos 2t + 3, 0 t 2 and show the amplitude, peri
Exam 2 Solutions
92.138 203 Calculus for the Life Sciences I
Spring 2014
1. The diagram below shows the graph of the function f .
(a) Is f (x1 ) > 0, = 0 or < 0?
f (x1 ) < 0.
(b) Is f (x1 ) > 0, = 0 or < 0?
f (x1 ) < 0.
(c) Is f increasing or decreasing a