The data displayed by the bar graph can be described by the mathematical model Percentage of College Freshmen with an Average Grade of A (A- to A+) in High School 4x p= + 29 where x is the number of years after 1980 and p is the percentage of college freshmen in a certain area who 5 70- had an average grade of A in high school. Use this information to answer parts (a) and (b) below. 56% 59% 60- 50 43% 40- 3 29% 30% 30- 8 20- 10- 1980 1990 2000 2010 20O13 Year a. According to the formula, in 2010, what percentage of college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much? According to the formula, % of college freshmen had an average grade of A in high school. The model V the actual value by % (Simplify your answer.) b. If trends shown by the formula continue, project when 61% of college freshmen will have had an average grade of A in high school. The year predicted is. (Type a whole number.)
The data displayed by the bar graph can be described by the mathematical model Percentage of College Freshmen with an Average Grade of A (A- to A+) in High School 4x p= + 29 where x is the number of years after 1980 and p is the percentage of college freshmen in a certain area who 5 70- had an average grade of A in high school. Use this information to answer parts (a) and (b) below. 56% 59% 60- 50 43% 40- 3 29% 30% 30- 8 20- 10- 1980 1990 2000 2010 20O13 Year a. According to the formula, in 2010, what percentage of college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much? According to the formula, % of college freshmen had an average grade of A in high school. The model V the actual value by % (Simplify your answer.) b. If trends shown by the formula continue, project when 61% of college freshmen will have had an average grade of A in high school. The year predicted is. (Type a whole number.)
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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![**Description and Analysis of College Freshmen Academic Performance**
The data displayed in the given bar graph can be described by the mathematical model:
\[ p = \frac{4x}{5} + 29 \]
where \( x \) is the number of years after 1980 and \( p \) is the percentage of college freshmen in a certain area who had an average grade of A in high school. Use this information to answer parts (a) and (b) below.
**Bar Graph Explanation:**
The bar graph is titled "Percentage of College Freshmen with an Average Grade of A (A- to A+) in High School." It displays data for the years 1980, 1990, 2000, 2010, and 2013.
- 1980: 29%
- 1990: 30%
- 2000: 43%
- 2010: 56%
- 2013: 59%
**Questions and Calculations:**
**a. According to the formula, in 2010, what percentage of college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much?**
According to the formula:
\[ p = \frac{4x}{5} + 29 \]
For the year 2010, \( x = 2010 - 1980 = 30 \).
Substitute \( x \) into the formula:
\[ p = \frac{4(30)}{5} + 29 = \frac{120}{5} + 29 = 24 + 29 = 53 \]
According to the formula, **53%** of college freshmen had an average grade of A in high school in 2010. The bar graph shows 56%.
Compare the model's prediction with the actual value:
\[ \text{Difference} = 56 - 53 = 3 \]
The model **underestimates** the actual value by **3%**.
**b. If trends shown by the formula continue, project when 61% of college freshmen will have had an average grade of A in high school.**
We need to find the year when \( p = 61 \):
\[ 61 = \frac{4x}{5} + 29 \]
Isolate \( x \):
\[ 61 - 29 = \frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f07c76b-37f9-44fb-a83a-7b9326898976%2F29ebc217-1ee8-4f87-afaf-005723d5c71e%2F3jo7d0b_processed.png&w=3840&q=75)
Transcribed Image Text:**Description and Analysis of College Freshmen Academic Performance**
The data displayed in the given bar graph can be described by the mathematical model:
\[ p = \frac{4x}{5} + 29 \]
where \( x \) is the number of years after 1980 and \( p \) is the percentage of college freshmen in a certain area who had an average grade of A in high school. Use this information to answer parts (a) and (b) below.
**Bar Graph Explanation:**
The bar graph is titled "Percentage of College Freshmen with an Average Grade of A (A- to A+) in High School." It displays data for the years 1980, 1990, 2000, 2010, and 2013.
- 1980: 29%
- 1990: 30%
- 2000: 43%
- 2010: 56%
- 2013: 59%
**Questions and Calculations:**
**a. According to the formula, in 2010, what percentage of college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much?**
According to the formula:
\[ p = \frac{4x}{5} + 29 \]
For the year 2010, \( x = 2010 - 1980 = 30 \).
Substitute \( x \) into the formula:
\[ p = \frac{4(30)}{5} + 29 = \frac{120}{5} + 29 = 24 + 29 = 53 \]
According to the formula, **53%** of college freshmen had an average grade of A in high school in 2010. The bar graph shows 56%.
Compare the model's prediction with the actual value:
\[ \text{Difference} = 56 - 53 = 3 \]
The model **underestimates** the actual value by **3%**.
**b. If trends shown by the formula continue, project when 61% of college freshmen will have had an average grade of A in high school.**
We need to find the year when \( p = 61 \):
\[ 61 = \frac{4x}{5} + 29 \]
Isolate \( x \):
\[ 61 - 29 = \frac{
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