Problem 1 :
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is
y = -0.2x + 1
a) Graph the equation
b) Interpret the x and y-intercepts.
c) After how many hours is the battery power at 75%.
Solution :
y = -0.2x + 1
a) From the equation above, we know that y-intercept is 1 and slope is 0.2. We can draw the falling line.
b) y = -0.2x + 1
x-intercept Put y = 0 -0.2x + 1 = 0 -0.2x = -1 x = 1/0.2 x = 5 |
y-intercept Put x = 0 -0.2(0) + 1 = y 0 + 1 = y y = 1 |
The x-intercept is 5. So, the battery lasts 5 hours. The y-intercept is 1. So, the battery power is at 100% when you turn on the laptop
c) x - number of hours, y - remaining quantity of battery power
Remaining quantity of battery power = 75% ==> 0.75
-0.2x + 1 = 0.75
-0.2x = 0.75 - 1
-0.2x = -0.25
x = 0.25/0.2
x = 1.25
After 1.25 hours, the battery will have power of 75%.
Problem 2 :
The amount y (in gallons) of gasoline remaining in a gas tank after driving x hours is
y = −2x + 12
(a) Graph the equation.
(b) Interpret the x- and y-intercepts.
(c) After how many hours are there 5 gallons left?
Solution :
a) Slope = -2, y-intercept = 12
Since it has negative slope, it must be a falling line.
b) y = −2x + 12
x-intercept Put y = 0 -2x + 12 = 0 2x = 12 x = 12/2 x = 6 |
y-intercept Put x = 0 -2(0) + 12 = y 0 + 12 = y y = 12 |
After 6 hours only, the quantity of gasoline will become 0.
Initially capacity of the tank is 12 gallons.
c) Number of gallons left = 5
-2x + 12 = 5
-2x = 5 - 12
-2x = -7
x = 7/2
x = 3.5
After 3.5 hours gallons left.
Problem 3 :
The graph relates temperatures y (in degrees Fahrenheit) to temperatures x (in degree Celsius)
a) Find the slope and y-intercept
b) Write an equation of the line
c) What is the mean temperature of Earth in degrees Fahrenheit)
Solution :
Slope :
To find slope, we choose any two points on the straight line.
(0, 32) and (30, 86)
y intercept is at 32.
b) Slope = 9/5
Equation of the line :
c) Mean temperature :
Problem 4 :
You are downloading a song. The percent y (in decimal form) of megabytes remaining to download after x seconds is
y = −0.1x + 1.
a) Graph the equation.
b) Interpret the x- and y-intercepts.
c) After how many seconds is the download 50% complete?
Solution :
a) Slope = -0.1 and y-intercept is 1
Since we have negative slope, it must be a falling line.
b) Interpret the x- and y-intercepts.
y = −0.1x + 1
x-intercept Put y = 0 -0.1x + 1 = 0 -0.1x = -1 x = 1/0.1 x = 10 |
y-intercept Put x = 0 -0.1(0) + 1 = y 1 = y y = 1 |
c) After how many seconds is the download 50% complete?
y = 50% = 0.50
0.50 = -0.1x + 1
0.50 - 1 = -0.1x
-0.50 = -0.1x
x = 5
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM