A certain investment is subject to continuous compounding. The value of the investment after t years is given by V = 6000e0.07 dollars. (a) Make a graph of the value of the investment over the first 20 years. V V 25 000 20 000 15 000 10000 5000 25 000 20 000 15 000 10000 5000 5 10 15 20 t 25 000 20 000 15 000 10000 5000 5 10 15 20 t 25 000 20 000 15 000 10000 5000 5 10 15 20 t
A certain investment is subject to continuous compounding. The value of the investment after t years is given by V = 6000e0.07 dollars. (a) Make a graph of the value of the investment over the first 20 years. V V 25 000 20 000 15 000 10000 5000 25 000 20 000 15 000 10000 5000 5 10 15 20 t 25 000 20 000 15 000 10000 5000 5 10 15 20 t 25 000 20 000 15 000 10000 5000 5 10 15 20 t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
(b)
Is the graph concave up or concave down?
concave upconcave down
(c)
Explain in practical terms what the concavity means.
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 increasing at a decreasing rate, so it grows less 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.
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.
The value of the investment is decreasing at an increasing rate, so it shrinks more rapidly in later years than 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 = 6000e⁰.07€ dollars.
(a) Make a graph of the value of the investment over the first 20 years.
V
V
25 000
20 000
15 000
10000
5000
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t
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20 000
15 000
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5
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t
25 000
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