The number of grams, f, of dietary fiber recommended daily for children depends on the age, a, of the child, as shown in the following table. Find an equation for f in terms of a.
The table looks like this (not sure how it will show up)
Column on left: Column on right:
Age of child, a Grams of Dietary Fiber
(in years) Recommended Daily, f
3 8
4 9
5 10
6 11
7 12
8 13
I need an equation in terms of dietary fiber, so I know it's going to be f = but from there I don't know what??
Thank you
f = a + 5
could you explain how you got the + 5 please?
he age numbers are all five less than the corresponding fiber numbers
To find an equation for f in terms of a, we need to determine the pattern or relationship between the age of the child (a) and the grams of dietary fiber recommended daily (f).
Looking at the table, we can observe that as the age of the child increases by 1 year, the recommended grams of dietary fiber also increase by 1. This implies a linear relationship between a and f.
To find the equation, we can consider the trend as a linear function. Since the table starts at age 3, we can define our equation in terms of a relative to this starting point. Let's call the equation f = ma + c, where m is the slope and c is the y-intercept.
From the table, we can see that when a = 3, f = 8. This gives us one point (3, 8) on the line.
Using another point, when a = 4, f = 9, we can substitute these values into the equation: 9 = m(4) + c.
Now we have two equations:
1) 8 = m(3) + c
2) 9 = m(4) + c
To eliminate c, we can subtract equation 1 from equation 2:
9 - 8 = (m(4) + c) - (m(3) + c)
1 = m(4 - 3)
1 = m
So we have found that the slope, m, is equal to 1.
To find the y-intercept, c, we can substitute the value of m back into equation 1:
8 = 1(3) + c
8 = 3 + c
c = 8 - 3
c = 5
Therefore, the equation in terms of f and a is:
f = a + 5