6 white & 4 brown
Step-by-step explanation:
Part A)
The slope m is 15.
This means that $15 is deposited into the bank account each day.
Part B)
Point-slope form:
Slope-intercept form:
Standard Form:
Part C)
Part D)
After 12 days, the balance of the bank account will be $505.
Step-by-step explanation:
We are given a table of values that lists x, the number of days that have passed, and g(x), the balance of the bank account.
The table represents a linear function.
Part A)
To find the slope, we can use the slope formula:
Where (x₁, y₁) and (x₂, y₂) are two points.
So, let’s pick two points from our table. We can use (0, 325) and (5, 400).
Let (0, 325) be (x₁, y₁) and let (5, 400) be (x₂, y₂). Substitute the values into the slope formula:
Evaluate:
So, the slope is 15 (or, more precisely, 15/1).
This means that $15 gets deposited into the bank account each day.
Part B)
We want to write the equation of the line in point-slope form, slope-intercept form, and standard form.
A) Point-slope form is given by:
Where m is the slope and (x₁, y₁) is a point.
We will substitute 15 for m.
We can use any point, but let’s use (0, 325) for (x₁, y₁) for consistency. Hence:
And this is point-slope form. You may choose to simplify the zero.
For reference, here are the other two forms possible given the table:
B) Slope-intercept form is given by:
Where m is the slope and b is the y-intercept.
Remember that the y-intercept is where x=0.
From our table, we can see that when x=0, y=325.
Therefore, our y-intercept is 325.
So, we will substitute 325 for b.
And we will also substitute 15 for m. Therefore:
C) Standard form is given by:
Where A, B, and C are integers, and A is positive.
We can start with the slope-intercept form:
And convert this to standard form. Subtract 15x from both sides:
Since A should be positive, multiply everything by -1. Hence:
Part C)
We can use the slope-intercept form:
Since our dependent variable, y, is the output of our function, y is the same as g(x).
Therefore, we can substitute g(x) for y to acquire:
Part D)
We can use our function. We want to find the balance after 12 days. Hence x=12.
Therefore:
Evaluate:
After 12 days, the balance in the bank account is $505.