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Find a possible formula for the exponential function described. An investment initially worth $5000 grows by 10% over a 9-year period. Round your answer for b to four decimal places. V (t) = ab', where: a = %3D Note that "V (t) =" is already provided. Do not include this in your submitted response to this question. V (t) = Edit

Find a possible formula for the exponential function described. An investment initially worth $5000 grows by 10% over a 9-year period. Round your answer for b to four decimal places. V (t) = ab', where: a = %3D Note that "V (t) =" is already provided. Do not include this in your submitted response to this question. V (t) = Edit

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Exponential Growth of an Investment** In this exercise, we aim to find a possible formula for the exponential function describing the growth of an investment. ### Problem Description An investment initially worth $5000 grows by 10% over a 9-year period. ### Goal Round your answer for \( b \) to four decimal places. ### Exponential Function Formula The formula for the value of the investment \( V(t) \) over time \( t \) is given by: \[ V(t) = ab^t \] Where: - \( a \) is the initial value of the investment. - \( b \) is the growth factor per time period. ### Variables to be Determined - \( a = \) (initial value of the investment) - \( b = \) (growth factor) **Note**: The form " \( V(t) = \) " is already provided. Do not include this in your submitted response. ### Submission Input the formula with correct values of \( a \) and \( b \) in the format provided below: \[ V(t) = \text{{your formula here}} \] Click the "Edit" button to input your response. **Interactive Component:** ![Edit Button](https://www.example.com/edit-button.jpg) By clicking the "Edit" button, you can input your calculated formula after determining the exponential growth factors correctly. For instructional purposes, if there are any graphs or diagrams: 1. **Graph of Exponential Function**: A graph illustrating \( V(t) = ab^t \) would typically show an upward curve, demonstrating the exponential growth of the investment over the 9-year period. The X-axis represents time (t), while the Y-axis represents the investment value \( V(t) \). By understanding and applying the principles of exponential growth, you can accurately model the future value of investments subjected to consistent percentage growth rates over time.
Transcribed Image Text:**Exponential Growth of an Investment** In this exercise, we aim to find a possible formula for the exponential function describing the growth of an investment. ### Problem Description An investment initially worth $5000 grows by 10% over a 9-year period. ### Goal Round your answer for \( b \) to four decimal places. ### Exponential Function Formula The formula for the value of the investment \( V(t) \) over time \( t \) is given by: \[ V(t) = ab^t \] Where: - \( a \) is the initial value of the investment. - \( b \) is the growth factor per time period. ### Variables to be Determined - \( a = \) (initial value of the investment) - \( b = \) (growth factor) **Note**: The form " \( V(t) = \) " is already provided. Do not include this in your submitted response. ### Submission Input the formula with correct values of \( a \) and \( b \) in the format provided below: \[ V(t) = \text{{your formula here}} \] Click the "Edit" button to input your response. **Interactive Component:** ![Edit Button](https://www.example.com/edit-button.jpg) By clicking the "Edit" button, you can input your calculated formula after determining the exponential growth factors correctly. For instructional purposes, if there are any graphs or diagrams: 1. **Graph of Exponential Function**: A graph illustrating \( V(t) = ab^t \) would typically show an upward curve, demonstrating the exponential growth of the investment over the 9-year period. The X-axis represents time (t), while the Y-axis represents the investment value \( V(t) \). By understanding and applying the principles of exponential growth, you can accurately model the future value of investments subjected to consistent percentage growth rates over time.
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