Suppose a person invested 1 million dollars in a certain project in the beginning of year 2000. The investment is a huge success and is now worth 10 million dollars at the end of year 2020. Assume that the investment has constant growth rate throughout the 20 years. Express the total worth of the investment W (in millions) as a function of time t (in years) and find the annual growth rate.
Suppose a person invested 1 million dollars in a certain project in the beginning of year 2000. The investment is a huge success and is now worth 10 million dollars at the end of year 2020. Assume that the investment has constant growth rate throughout the 20 years. Express the total worth of the investment W (in millions) as a function of time t (in years) and find the annual growth rate.
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 9E
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Suppose a person invested 1 million dollars in a certain project in the beginning of year 2000. The investment is a huge success and is now worth 10 million dollars at the end of year 2020. Assume that the investment has constant growth rate throughout the 20 years.
Express the total worth of the investment W (in millions) as a function of time t (in years) and find the annual growth rate.
Expert Solution
Step 1
Let the Investment at time t be: W(t).
Investment has constant growth rate throughout the 20 years. Therefore:
where k is the growth rate.
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