A certain investment is subject to continuous compounding. The value of the investment after t years is given by V- 7000e.05t dollars.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 40E
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A certain investment is subject to continuous compounding. The value of the investment after t years is given by
V = 7000e"
0.05t dollars.
(a) Make a graph of the value of the investment over the first 20 years.
20 000
20 000
15 000
15 000-
10 000-
10000-
5000
5000
10
15
20
5
10
15
20
20 000
20 000
15 000
15 000
10 000
1000아
5000
5000
5
10
15
20
10
15
20
(b) Is the graph concave up or concave dovwn?
concave up
O concave down
Explain in practical terms what the concavity means.
The value of the investment is decreasing at an increasing rate, so it shrinks more rapidly in later years than in earlier years.
The value of the investment is increasing at an increasing rate, so it grows more rapidly in later years than in earlier years.
The value of the investment is decreasing at a decreasing rate, so it shrinks less rapidly in later years than in earlier years.
O The value of the investment is increasing at a decreasing rate, so it grows less rapidly in later years than in earlier years.
O The value of the investment is increasing at a constant rate, so it grows at the same rate in later years as it does in earlier years.
Transcribed Image Text:A certain investment is subject to continuous compounding. The value of the investment after t years is given by V = 7000e" 0.05t dollars. (a) Make a graph of the value of the investment over the first 20 years. 20 000 20 000 15 000 15 000- 10 000- 10000- 5000 5000 10 15 20 5 10 15 20 20 000 20 000 15 000 15 000 10 000 1000아 5000 5000 5 10 15 20 10 15 20 (b) Is the graph concave up or concave dovwn? concave up O concave down Explain in practical terms what the concavity means. The value of the investment is decreasing at an increasing rate, so it shrinks more rapidly in later years than in earlier years. The value of the investment is increasing at an increasing rate, so it grows more rapidly in later years than in earlier years. The value of the investment is decreasing at a decreasing rate, so it shrinks less rapidly in later years than in earlier years. O The value of the investment is increasing at a decreasing rate, so it grows less rapidly in later years than in earlier years. O The value of the investment is increasing at a constant rate, so it grows at the same rate in later years as it does in earlier years.
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