Chapter 3.7, Problem 35PPS

To determine

To write: A step function for the number of smoothies that can be bought with x dollars and calculate the number of smoothies that can be bought with $10.

Answer to Problem 35PPS

The step function for the above question is given by

  $f(x)=\left[\frac{x}{3.79}\right]$ .................. (1)

For $10 the number of smoothies that can be bought =2.

Explanation of Solution

Given information: cost of 1 smoothie is $3.79.

Formula used:

  $f(x)=\left[x\right],\text{where}\left[x\right]\text{indicates the}\text{greatest integer}\text{part of}x$

The function rounds -off the real number down to the integer less than the number

For example:

  $\begin{array}{l}\text{If}x=6.357,\text{then}[x]=6\hfill \\ \text{If}x=-6.357,\text{then}[x]=-7\hfill \end{array}$

Calculation:

Since for 1 smoothie the cost = $3.79

So for x dollars, the number of smoothie that can be bought = $f(x)=\left[\frac{x}{3.79}\right]$

Hence the step function for the above question is given by

  $f(x)=\left[\frac{x}{3.79}\right]$ .................. (1)

So for $10 the number of smoothies that can be bought will be

  $\begin{array}{c}f(10)=\left[\frac{10}{3.79}\right]\\ =\left[2.63\right]\\ =2\end{array}$