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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.

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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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.
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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