VENTURE-CAPITAL INVESTMENT Venture-capital investment increased dramatically in the late 1990s but came to a screeching halt after the dot-com bust. The venture-capital investment (in billions of dollars) from 1995 ( t = 0) through 2003 ( t = 8) is approximated by the function C ( t ) = { 0.6 t 2 + 2.4 t + 7.6 if 0 ≤ t < 3 3 t 2 + 18.8 t − 63.2 if 3 ≤ t < 5 − 3.3167 t 3 + 80.1 t 2 − 642.583 t + 1730.8025 if 5 ≤ t < 8 a. In what year did venture-capital investment peak over the period under consideration? What was the amount of that investment? b. In what year was the venture-capital investment lowest over this period? What was the amount of that investment? Hint: Find the absolute extrema of C on each of the closed intervals [0, 3], [3, 5], and [5, 8]. Sources: Venture One: Ernst & Young.
VENTURE-CAPITAL INVESTMENT Venture-capital investment increased dramatically in the late 1990s but came to a screeching halt after the dot-com bust. The venture-capital investment (in billions of dollars) from 1995 ( t = 0) through 2003 ( t = 8) is approximated by the function C ( t ) = { 0.6 t 2 + 2.4 t + 7.6 if 0 ≤ t < 3 3 t 2 + 18.8 t − 63.2 if 3 ≤ t < 5 − 3.3167 t 3 + 80.1 t 2 − 642.583 t + 1730.8025 if 5 ≤ t < 8 a. In what year did venture-capital investment peak over the period under consideration? What was the amount of that investment? b. In what year was the venture-capital investment lowest over this period? What was the amount of that investment? Hint: Find the absolute extrema of C on each of the closed intervals [0, 3], [3, 5], and [5, 8]. Sources: Venture One: Ernst & Young.
VENTURE-CAPITAL INVESTMENT Venture-capital investment increased dramatically in the late 1990s but came to a screeching halt after the dot-com bust. The venture-capital investment (in billions of dollars) from 1995 (t = 0) through 2003 (t = 8) is approximated by the function
C
(
t
)
=
{
0.6
t
2
+
2.4
t
+
7.6
if 0
≤
t
<
3
3
t
2
+
18.8
t
−
63.2
if 3
≤
t
<
5
−
3.3167
t
3
+
80.1
t
2
−
642.583
t
+
1730.8025
if 5
≤
t
<
8
a. In what year did venture-capital investment peak over the period under consideration? What was the amount of that investment?
b. In what year was the venture-capital investment lowest over this period? What was the amount of that investment?
Hint: Find the absolute extrema of C on each of the closed intervals [0, 3], [3, 5], and [5, 8].
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