Question

Research linear, quadratic, and exponential functions using the Internet. For each of the three types of functions, provide an example of a problem/situation you found on the Internet
where that function was used to model the situation or answer the problem. Include the actual function used in the example and web page where you found the example.

Answer 1

Answer:

1. LINEAR FUNCTIONS

Example is A cab company charges a $5 boarding rate in addition to its meter which is $3 for every mile.  

WEBSITE

https://www.mathwarehouse.com/algebra/linear_equation/real-world-application.php#ixzz65x3vQnRq

This is a linear function of the form y = 5 + 3x. The answer is modeled with a straight-line graph.

2. QUADRATIC FUNCTIONS

Example: Throwing a Ball

A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. When does it hit the ground?

WEBSITE

https://www.mathsisfun.com/algebra/quadratic-equation-real-world.html#:~:targetText=Balls%2C%20Arrows%2C%20Missiles%20and%20Stones,its%20position%20at%20all%20times!

This is a quadratic function of the form $3 + 14t - 5t^{2} = 0$ . The answer is modelled with a parabola graph.

3. EXPONENTIAL FUNCTIONS

Example: For her eighth birthday, Shelley’s grandmother gave her a full bag of candy. Shelley counted her candy and found out that there were 160 pieces in the bag. As you might suspect, Shelley loves candy, so she ate half the candy on the first day. Then her mother told her that if she eats it at that rate, the candy will only last one more day—so Shelley devised a clever plan. She will always eat half of the candy that is left in the bag each day. She thinks that this way she can eat candy every day and never run out.

How much candy does Shelley have at the end of the week? Will the candy really last forever?

WEBSITE

https://www.ck12.org/book/CK-12-Algebra-I-Second-Edition/section/8.7/

This is an exponential function of the form $y = 160 ( \frac{1}{2} )^{x}$.

The answer is modelled by a decaying graph function and with an asymptote at y = 0

Step-by-step explanation:

1. Linear function is any function that graphs to a straight line and has no exponents. It is a polynomial function with degree one or zero.

Normally of the form y = mx + c, where y and x are the variables, m the gradient and c the intercept

2. Quadratic functions are polynomial functions with one or more variables where the highest-degree term is of the second degree. The graph of a quadratic function normally graphs to a conic section (a circle or other ellipse, a parabola, or a hyperbola)

Normally of the form $y= ax^{2} +bx +c$. where y and x are the variables, a,b,c are constants

3. Exponential functions are functions which the argument is an exponent. As a function of a real variable, exponential functions are characterized by the fact that the growth rate of such a function (that is, its derivative) is directly proportional to the value of the function.

Normally of the form $y = ab^{x}$