Question

Identify whether the following real world examples should be modeled by a linear quadratic or exponential function

Answer 1

Solution

- Linear:

The general form of a linear function is

$\begin{gathered} y=ax+b \\ where, \\ a,\text{ and b are constants} \end{gathered}$

- Quadratic:

The general form of a quadratic function is:

$\begin{gathered} y=ax^2+bx+c \\ where, \\ a,b,c\text{ are constants} \end{gathered}$

- Exponential:

The general form of an exponential function is:

$\begin{gathered} y=ab^x \\ where, \\ a,b\text{ are constants} \end{gathered}$

- Now that we know the general forms of these functions, we can proceed to solve the question.

- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works

- Let us imagine that a person receives $a for every hour worked.

- This means that:

After 1 hour, the person makes $a

After 2 hours, the person makes $a + $a = $2a

After 3 hours, the person makes $a + $a +$a = $3a

- We can therefore generalize as follows:

Thus, after x hours, the person makes:

$x\times a=\ ax$

- Thus, the function representing the amount a person makes per hour of work is given by:

$y=ax$

- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function

Final Answer

The answer is Linear