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6) The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situati A) exponential B) Linear C) quadratic D) radical

6) The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situati A) exponential B) Linear C) quadratic D) radical

Advanced Engineering Mathematics
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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### Understanding Growth Functions: Salary Increment Scenario **Question: 6** The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situation? - **A) Exponential** - **B) Linear** - **C) Quadratic** - **D) Radical** --- **Explanation:** In this scenario, the delivery driver's salary increases by a fixed percentage (3%) each year. This type of growth is typically best modeled by an **Exponential** function. ### Justifications: - **Exponential Growth:** Occurs when a quantity increases by the same rate (percentage) over equal intervals of time. The function has the general form \( P(t) = P_0 \times (1 + r)^t \), where \( P_0 \) is the initial amount, \( r \) is the rate of increase, and \( t \) is the time period. - **Linear Growth:** Represents a constant increase over time, which adds a fixed amount each period. - **Quadratic Growth:** Involves a variable increase that follows a squared term. - **Radical Growth:** Involves functions whose rates of change diminish over time and follow a root function. Since our problem involves a fixed percentage increase, we select **Option A: Exponential** as the best model for the situation.
Transcribed Image Text:### Understanding Growth Functions: Salary Increment Scenario **Question: 6** The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which type of function best models this situation? - **A) Exponential** - **B) Linear** - **C) Quadratic** - **D) Radical** --- **Explanation:** In this scenario, the delivery driver's salary increases by a fixed percentage (3%) each year. This type of growth is typically best modeled by an **Exponential** function. ### Justifications: - **Exponential Growth:** Occurs when a quantity increases by the same rate (percentage) over equal intervals of time. The function has the general form \( P(t) = P_0 \times (1 + r)^t \), where \( P_0 \) is the initial amount, \( r \) is the rate of increase, and \( t \) is the time period. - **Linear Growth:** Represents a constant increase over time, which adds a fixed amount each period. - **Quadratic Growth:** Involves a variable increase that follows a squared term. - **Radical Growth:** Involves functions whose rates of change diminish over time and follow a root function. Since our problem involves a fixed percentage increase, we select **Option A: Exponential** as the best model for the situation.
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