An assembly line in a factory makes roofing nails. After 8 days, the total number of nails produced is 100,000. After another 4 days (on day 12), a total of 148,000 nails is produced.
Which equation models the total number of nails produced?
y=8x+148,000
y=−8x+100,000
y=−12,000x+4000
y=12,000x+4000
they made 48000 nails in 4 days, or 12000 per day
(D) is the only equation with slope = 12000
or, doing the point-slope form
y-100,000 = 12000(x-8)
which is indeed (D)
Thanks oobleck.
To find the equation that models the total number of nails produced, we need to analyze the given information and identify the pattern or relationship between the number of days and the total number of nails produced.
From the information provided, we know that after 8 days, the total number of nails produced is 100,000. This means that in 8 days, the assembly line produces 100,000 nails.
After another 4 days (on day 12), the total number of nails produced is 148,000. This means that in the next 4 days (from day 9 to day 12), the assembly line produces an additional 48,000 nails.
To find the rate at which the assembly line produces nails, we can calculate the change in the total number of nails produced per day. We can calculate this by dividing the change in the total number of nails produced (48,000) by the number of days (4).
Change in nails produced per day = (148,000 - 100,000) / (12 - 8) = 48,000 / 4 = 12,000
Now that we know the rate at which the assembly line produces nails is 12,000 per day, we can form the equation.
The equation that models the total number of nails produced is:
y = 12,000x + 100,000
In this equation, 'y' represents the total number of nails produced and 'x' represents the number of days. The constant term, 100,000, represents the initial number of nails produced after 8 days. The coefficient of 'x', 12,000, represents the rate at which the assembly line produces nails per day.