Totally lost on this. Any help would be awesome!
1. The function
A(t)=0.233t+5.87
can be used to estimate the median age of cars in the United States t years after 1990. (In this context, we mean that if the median age of cars is 3 yr, then half the cars are older than 3 yr and half are younger.) Show your work and explain your answer.
a. Find the median age of cars in 2002.
b. In what year was the median age of cars 7.734 yr?
2. Homespun Jellies charges $2.49 for each jar of preserves. Shipping charges are $3.75 for handling, plus $0.60 per jar. Find a linear function for determining the cost of buying and shipping x jars of preserves. Show your work and explain your answer.
3. The table below shows data regarding the world indoor records in the men’s 400-m run.
1970 4.68
2004 44.63
a. Use the two data points to find a linear function that fits the data. Let the number of years since 1970 and the world record x years from 1970. Show your work and explain your answer.
b. Use the function to estimate the world record in the men’s 400-m run in 2008 and in 2010. Show your work and explain your answer.
4. Find an equation of the line containing the given pair of points: (-2 ,3) and
(-4, 6). Show your work.
Rick,
These questions are all very similar. They are all about straight lines on a graph of form
y = m x + b
where m is the slope and b is the y intercept (the value of y when x = 0)
I will show you how to do one of them. Then you do the rest.
[ I was going to do #3 but you have a typo in the 1970 time ]
2. Homespun Jellies charges $2.49 for each jar of preserves. Shipping charges are $3.75 for handling, plus $0.60 per jar. Find a linear function for determining the cost of buying and shipping x jars of preserves. Show your work and explain your answer.
cost = .6 x + 3.79
too easy
1. The function
A(t)=0.233t+5.87
can be used to estimate the median age of cars in the United States t years after 1990. (In this context, we mean that if the median age of cars is 3 yr, then half the cars are older than 3 yr and half are younger.) Show your work and explain your answer.
a. Find the median age of cars in 2002.
2002-1990 = 12 years after 1990
A = .233(12) + 5.87
= 2.676+5.87
=8.546
b. In what year was the median age of cars 7.734 yr?
7.734 = .233 t +5.87
solve for t
add t to 1990
1. a. To find the median age of cars in 2002, substitute t = 2002 - 1990 = 12 into the function A(t) = 0.233t + 5.87:
A(12) = 0.233(12) + 5.87
A(12) = 2.796 + 5.87
A(12) = 8.666
Therefore, the median age of cars in 2002 is approximately 8.666 years.
b. To find the year when the median age of cars is 7.734 years, we need to solve the equation A(t) = 7.734:
0.233t + 5.87 = 7.734
0.233t = 7.734 - 5.87
0.233t = 1.864
t ≈ 1.864 / 0.233
t ≈ 8
So, the median age of cars was 7.734 years 8 years after 1990, which is in the year 1998.
2. Let C(x) be the cost of buying and shipping x jars of preserves. We know that the shipping charges are $3.75 for handling, plus $0.60 per jar. Therefore, the linear function for determining the cost can be expressed as:
C(x) = 2.49x + 3.75 + 0.60x
C(x) = 3.09x + 3.75
So, the linear function for determining the cost of buying and shipping x jars of preserves is C(x) = 3.09x + 3.75.
3. a. We can use the two data points (1970, 4.68) and (2004, 44.63) to find the linear function that fits the data. Let the number of years since 1970 be x, and the world record x years from 1970 be y. We can form the following equation:
y = mx + b
Using the two data points, we can find the slope (m) and y-intercept (b) of the line:
m = (44.63 - 4.68) / (2004 - 1970)
m = 39.95 / 34
m ≈ 1.175
Using the point-slope form of a linear equation, we can plug in one of the points to find the y-intercept (b):
4.68 = 1.175(1970) + b
4.68 = 2318.25 + b
b = 4.68 - 2318.25
b ≈ -2313.57
Therefore, the linear function that fits the data is y = 1.175x - 2313.57.
b. To estimate the world record in the men's 400-m run in 2008 and 2010, we can substitute x = 2008 - 1970 = 38 and x = 2010 - 1970 = 40 into the linear function:
For 2008:
y = 1.175(38) - 2313.57
y ≈ 44.725
For 2010:
y = 1.175(40) - 2313.57
y ≈ 46.725
Therefore, the estimated world record in the men's 400-m run in 2008 is approximately 44.725 seconds, and in 2010, it is approximately 46.725 seconds.
4. To find the equation of the line containing the given pair of points (-2, 3) and (-4, 6), we can use the point-slope form of a linear equation:
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (-4 - -2)
m = 3 / -2
m = -1.5
Using one of the points and the slope, we can find the y-intercept (b) using the point-slope form:
3 = -1.5(-2) + b
3 = 3 + b
b = 3 - 3
b = 0
Therefore, the equation of the line is y = -1.5x + 0, or simplified as y = -1.5x.
1. To find the median age of cars in 2002, we need to substitute the value of t = 2002 - 1990 = 12 into the function A(t) = 0.233t + 5.87:
A(12) = 0.233*12 + 5.87
A(12) = 2.796 + 5.87
A(12) = 8.666
Therefore, the median age of cars in 2002 is approximately 8.666 years.
To find the year when the median age of cars is 7.734 years, we need to solve the equation 7.734 = 0.233t + 5.87 for t:
7.734 - 5.87 = 0.233t
1.864 = 0.233t
t ≈ 8
Since t represents the number of years after 1990, we need to add 8 to 1990 to find the year:
1990 + 8 = 1998
Therefore, the median age of cars was approximately 7.734 years in the year 1998.
2. The cost of buying and shipping x jars of preserves can be found by adding the cost of the jars and the shipping charges together. The cost of the jars is calculated as $2.49 times the number of jars (x), and the shipping charges are a fixed cost of $3.75 for handling plus $0.60 per jar:
Cost(x) = (2.49 * x) + 3.75
Therefore, the linear function for determining the cost of buying and shipping x jars of preserves is Cost(x) = (2.49 * x) + 3.75.
3. To find a linear function that fits the data given in the table, we need to find the equation of the line that passes through the two data points: (1970, 4.68) and (2004, 44.63).
Let the number of years since 1970 be x, and the world record x years from 1970 be represented by y. We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, to find the linear function.
First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
m = (44.63 - 4.68) / (2004 - 1970)
m = 39.95 / 34 = 1.175
Next, find the y-intercept (b) by substituting one of the points into the equation y = mx + b:
4.68 = 1.175 * 1970 + b
4.68 = 2315.25 + b
b = 4.68 - 2315.25
b ≈ -2310.57
Therefore, the linear function that fits the data can be written as y = 1.175x - 2310.57.
To estimate the world record in the men's 400-m run in 2008 and 2010, substitute the corresponding values of x into the linear function:
For 2008 (x = 2008 - 1970 = 38):
y = 1.175 * 38 - 2310.57
y ≈ 44.85
For 2010 (x = 2010 - 1970 = 40):
y = 1.175 * 40 - 2310.57
y ≈ 46.75
Therefore, the estimated world record in the men's 400-m run in 2008 is approximately 44.85 seconds, and in 2010 is approximately 46.75 seconds.
4. To find the equation of the line containing the given pair of points (-2, 3) and (-4, 6), we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the given points, we have:
m = (6 - 3) / (-4 - (-2))
m = 3 / (-4 + 2)
m = 3 / (-2)
m = -1.5
Now that we have the slope (m), we can use the slope-intercept form of a line, y = mx + b, and substitute one of the points to find the y-intercept (b). Let's use the point (-2, 3):
3 = -1.5 * (-2) + b
3 = 3 + b
b = 0
Therefore, the equation of the line is y = -1.5x + 0, or simply y = -1.5x.