Q. 4.98 The equation T=14n+40聽is used t... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 4.98 (page 509)

The equation $T = \frac{1}{4} n + 40$ is used to estimate the temperature in degrees Fahrenheit, T, based on the number of cricket chirps, n, in one minute.
鈸� Estimate the temperature when there are no chirps.
鈸� Estimate the temperature when the number of chirps in one minute is $100$ .
鈸� Interpret the slope and T-intercept of the equation.
鈸� Graph the equation.

Short Answer

Expert verified

Part 鈸� Estimated temperature when there are no chirps is: $40$ degrees

Part 鈸� Estimated temperature when there are $100$ chirps a minute is: $65$ degrees

Part 鈸� The slope, $m = \frac{1}{4}$ , means that when the number of chirps increases by $4$ , temperature increases by one degree. The T-intercept means that temperature is $40$ degrees when the number of chirps is $0$ .

Part 鈸� Graph of the equation

Step by step solution

Part (a) Step 1. Given Information

The equation $T = \frac{1}{4} n + 40$ is used to estimate the temperature in degrees Fahrenheit, $T$ , based on the number of cricket chirps, $n$ , in one minute.

Part (a) Step 2. Estimating the temperature when there are no chirps

Put $n = 0$ in the given equation $T = \frac{1}{4} n + 40$

鈬� T = \frac{1}{4} (0) + 40 鈬� T = 0 + 40 鈬� T = 40

Part (b) Step 1. Estimating the temperature when the number of chirps in one minute is 100

Put $n = 100$ in the given equation $T = \frac{1}{4} n + 40$

鈬� T = \frac{1}{4} (100) + 40 鈬� T = 25 + 40 鈬� T = 65

Part (c) Step 1. Interpreting the slope and T-intercept of the equation

The equation $T = \frac{1}{4} n + 40$ is in slope-intercept form $y = m x + b$ .

By comparison, we get, slope, $m = \frac{1}{4}$ , which means that when number of cricket chirps increases by $4$ , the temperature increases by one degree. T-intercept means that estimated temperature is $40$ degrees when number of cricket chirps is $0$ .