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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 6DE
Related questions
Question
![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92e55b55-fe86-43b9-8068-0184a2158b73%2Fec7adb10-6eea-4b94-ab8c-da468be8f742%2F3olndc9_processed.jpeg&w=3840&q=75)
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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