Question

The value, v, of your quarters (in cents) is a function of n, the number of quarters you have.Identify the independent variablea) Draw a input-output diagram to represent this functionb. write an equation that represents this functionc. find the output when the input is 10d. identify the independent and dependent variables

Answer 1

b. v = 25n

c. v = 250

d. Independent variable: n

dependent variable: v

Step-by-step explanation:

Part a.

The value, v, of your quarter is a function of n, the number of quarters you have, so given a value of n, you can calculate the value of v.

If n = 1

v = 25

Because one quarter has a value of 25 cents.

If n = 2

v = 2(25) = 50

because two quartes has a value of 50 cents.

If n = 3

v = 3(25) = 75

Therefore, we can draw a diagram using the points (1, 25), (2, 50), and (3, 75) as follows

Part b.

Then, we can see that the value of your quartes is 25 times the number of quartes, so the equation that represents this function is

v = 25n

Part c.

To find the output when the input is 10, we need to replace n by 10 on the equation above

v = 25n

v = 25(10)

v = 250

So, the output is 250 cents

Part d.

The value of your quarters depends on the number of quarters you have, so the dependent variable is v, the value of your quarters and the independent variable is n, the number of quarters.