64. Business: growth of an investment. A company deter- mines that the value of an investment after t years is V, in millions of dollars, where Vis given by V(t) = 5t – 3012 + 45t + 5Vi. Note: Calculators often use only the variables y and x, so you may need to change the variables. a) Graph V over the interval [0, 5]. b) Find the equation of the secant line passing through the points (1, V(1)) and (5, V(5)). Then graph this secant line using the same axes as in part (a). c) Find the average rate of change of the investment between year 1 and year 5. d) Repeat parts (b) and (c) for the following pairs of points: (1, V(1)) and (4, V(4)); (1, V(1)) and (3, V(3)); (1, V(1)) and (1.5, V(1.5)). e) What appears to be the slope of the tangent line to the graph at the point (1, V(1))? f) Approximate the rate at which the value of the investment is changing at t = 1 yr.
64. Business: growth of an investment. A company deter- mines that the value of an investment after t years is V, in millions of dollars, where Vis given by V(t) = 5t – 3012 + 45t + 5Vi. Note: Calculators often use only the variables y and x, so you may need to change the variables. a) Graph V over the interval [0, 5]. b) Find the equation of the secant line passing through the points (1, V(1)) and (5, V(5)). Then graph this secant line using the same axes as in part (a). c) Find the average rate of change of the investment between year 1 and year 5. d) Repeat parts (b) and (c) for the following pairs of points: (1, V(1)) and (4, V(4)); (1, V(1)) and (3, V(3)); (1, V(1)) and (1.5, V(1.5)). e) What appears to be the slope of the tangent line to the graph at the point (1, V(1))? f) Approximate the rate at which the value of the investment is changing at t = 1 yr.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![64. Business: growth of an investment. A company deter-
mines that the value of an investment after t years is V,
in millions of dollars, where Vis given by
V(t) = 5t – 3012 + 45t + 5Vi.
Note: Calculators often use only the variables y and x, so
you may need to change the variables.
a) Graph V over the interval [0, 5].
b) Find the equation of the secant line passing through
the points (1, V(1)) and (5, V(5)). Then graph this
secant line using the same axes as in part (a).
c) Find the average rate of change of the investment
between year 1 and year 5.
d) Repeat parts (b) and (c) for the following pairs
of points: (1, V(1)) and (4, V(4)); (1, V(1)) and
(3, V(3)); (1, V(1)) and (1.5, V(1.5)).
e) What appears to be the slope of the tangent line to the
graph at the point (1, V(1))?
f) Approximate the rate at which the value of the
investment is changing at t = 1 yr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94ba4c5f-9a36-4fdf-b7f3-b12d095c2b52%2F5f716ea4-720e-4ff5-81ad-50fa5a8ee46d%2Fk6osc08_processed.png&w=3840&q=75)
Transcribed Image Text:64. Business: growth of an investment. A company deter-
mines that the value of an investment after t years is V,
in millions of dollars, where Vis given by
V(t) = 5t – 3012 + 45t + 5Vi.
Note: Calculators often use only the variables y and x, so
you may need to change the variables.
a) Graph V over the interval [0, 5].
b) Find the equation of the secant line passing through
the points (1, V(1)) and (5, V(5)). Then graph this
secant line using the same axes as in part (a).
c) Find the average rate of change of the investment
between year 1 and year 5.
d) Repeat parts (b) and (c) for the following pairs
of points: (1, V(1)) and (4, V(4)); (1, V(1)) and
(3, V(3)); (1, V(1)) and (1.5, V(1.5)).
e) What appears to be the slope of the tangent line to the
graph at the point (1, V(1))?
f) Approximate the rate at which the value of the
investment is changing at t = 1 yr.
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