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4.) A car company introduces a new car for which the number of cars sold S is the function S(t)=300 5- where t is the time in months. 9 t+2 a.) Find the average rate of cars sold over the first 12 months. b.) During what month does the average rate of cars sold equal the rate of change of car sales?

4.) A car company introduces a new car for which the number of cars sold S is the function S(t)=300 5- where t is the time in months. 9 t+2 a.) Find the average rate of cars sold over the first 12 months. b.) During what month does the average rate of cars sold equal the rate of change of car sales?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Educational Content on Car Sales Function** A car company introduces a new car for which the number of cars sold, \( S(t) \), is represented by the function: \[ S(t) = 300 \left( \frac{5t}{t+2} \right) \] where \( t \) is the time in months. **Questions:** a) Find the average rate of cars sold over the first 12 months. b) During what month does the average rate of cars sold equal the rate of change of car sales? **Instructions:** 1. **For Part (a):** To find the average rate of cars sold over the first 12 months, integrate \( S(t) \) from \( t = 0 \) to \( t = 12 \) and then divide by 12. 2. **For Part (b):** To address when the average rate of cars sold equals the rate of change of car sales, equate the derivative of \( S(t) \), \( S'(t) \), to the average rate and solve for \( t \).
Transcribed Image Text:**Educational Content on Car Sales Function** A car company introduces a new car for which the number of cars sold, \( S(t) \), is represented by the function: \[ S(t) = 300 \left( \frac{5t}{t+2} \right) \] where \( t \) is the time in months. **Questions:** a) Find the average rate of cars sold over the first 12 months. b) During what month does the average rate of cars sold equal the rate of change of car sales? **Instructions:** 1. **For Part (a):** To find the average rate of cars sold over the first 12 months, integrate \( S(t) \) from \( t = 0 \) to \( t = 12 \) and then divide by 12. 2. **For Part (b):** To address when the average rate of cars sold equals the rate of change of car sales, equate the derivative of \( S(t) \), \( S'(t) \), to the average rate and solve for \( t \).
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