# mathematics

Create an appropriate model for each situation below. Create your model and solve the problem. Show all calculations. Round to two decimal places unless stated otherwise.

1. A projectile’s motion can be modeled by the quadratic equation:

h = -gt² + v0t + h0where h = height from the ground; g = gravity constant (16 if units in ft; 4.9 if in meters); t = time in second elapsed from release of projectile; v0= initial velocity; h0= initial height. Write the equation for a projectile that is dropped (v0= 0) from a height of 100 ft. When will it hit the ground? Change the equation to reflect that the object is thrown upward from an initial height of 6 ft at 30 ft/sec. When will the object be back at the starting height? Hit the ground?

2. The speed of a vehicle can be determined from the length of the skid mark using the following formula: S = where S is the calculated speed and D is the length of the skid mark in feet. How fast was the vehicle traveling if it left a 210 ft skid mark? How long of a skid mark would a vehicle traveling at 45 mph make?

3. A group is going to a state fair. If children’s tickets are $7.50 per child and adult tickets are $12 per adult, how many of each can go to the fair for $200? Write a linear inequality, graph it, and show several solutions on your graph. Write at least 5 possible solutions.

**Suspension bridge project**

Most suspension bridges are approximately parabolic in shape in the main section of the bridge. The two towers for suspending the cable define the outer boundaries of the parabola. Using the data about the bridges from the table below, create an equation for the parabola, and graph the section between the towers for each bridge.

Name

Height of towers

Distance between towers

Location

Verrazano Narrows

693 ft

4260 ft

New York, NY

Golden Gate

746 ft

4200 ft

San Francisco, CA

Akashi-Kaikyo

979 ft

6532 ft

Kobe, Japan

**Finance models project**

Using the exponential model for compound interest earned periodically, solve the following. Assume all interest is compounded monthly unless otherwise given, and the interest rate is 2.625%. Remember to show all calculations and how you used the formula. Show what numbers you enter into the calculator.

1. Assume that you deposited $1000 in an investment account on your 18thbirthday. How much would you have in the account now? How much would you have on your 68thbirthday?

2. Assume the account was opened on your 25thbirthday; how much would be in the account on your 68thbirthday?

3. Assume the account is opened on your 40thbirthday; what is its value on your 68thbirthday?

4. Change the invested amount to $5000 and answer the questions above.

5. You want to have $1.5 million in the account on your 68thbirthday. How much would you need to invest at age 18 to reach your goal? Age 30? Age 50?

6. What would be your advice to anyone wanting to invest for retirement? Why?