1. Section 3.5 – Mathematical Modeling

2. Direct Variation -
Inverse Variation - x

3. Direct Variation -
Inverse Variation - x
5/4 5/16 5/36 5/64 1/20
5 5/4 5/9 5/16 1/50

4. Direct Variation - OR
Inverse Variation -
YES NO
DIRECT VARIATION

5. Direct Variation - OR
Inverse Variation - NO
YES
INVERSE VARIATION

6. Direct Variation -
Inverse Variation -
Directly Proportional -
If x = 2 and y = 14, write a linear model that relates y to x if y is
directly proportional to x.
If x = 6 and y = 580, write a linear model that relates y to x if y is
directly proportional to x.

7. The simple interest (I) on an investment is directly proportional
to the amount of the investment (P). By investing $5000 in a
municipal bond, you obtained an interest payment of $187.50
after one year. Find a mathematical model that gives the
interest (I) for this municipal bond after one year in terms of the
amount invested (P).

8. The distance a spring is stretched (or compressed) varies
directly as the force on the spring. A force of 220 newtons
stretches a spring 0.12 meters. What force is required to
stretch the spring 0.16 meters?

9. Direct Variation -
Inverse Variation -
Directly Proportional -
Write a mathematical model for each of the following:
A) y varies directly as the cube of x
B) h varies inversely as the square root of s
C) c is jointly proportional to the square of x and

10. Write a mathematical model for each of the following. In each
case, determine the constant of proportionality.
A) y varies directly as the cube of x. (y = 81 when x = 3)
B) h varies inversely as the square root of s. (h = 2 when s = 4)
C) c is jointly proportional to the square of x and
(c = 144 when x = 3 and y = 2)

11. Direct Variation -
Inverse Variation -
Directly Proportional -
The stopping distance d of an automobile is directly proportional
to the square of its speed s. A car required 75 feet to stop
when its speed was 30 mph. Estimate the stopping distance
if the brakes are applied when the car is traveling at 50 mph.