Question

Sales Taxes In a certain state, the sales tax $T$ on the amount of taxable goods is $6 \%$ of the value of the goods purchased $x$, where both $T$ and $x$ are measured in dollars. a. Express $T$ as a function of $x$. b. Find $T(200)$ and $T(5.65)$.

Name: Problem 66, Chapter 2: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-07-06T15:40:45-08:00
Duration: 1 min 13 s
Channel: Carson Merrill
Description: Sales Taxes In a certain state, the sales tax T on the amount of taxable goods is 6 % of the value of the goods purchased x, where both T and x are measured in dollars. a. Express T as a function of x. b. Find T(200) and T(5.65).

   Sales Taxes In a certain state, the sales tax $T$ on the amount of taxable goods is $6 \%$ of the value of the goods purchased $x$, where both $T$ and $x$ are measured in dollars.
a. Express $T$ as a function of $x$.
b. Find $T(200)$ and $T(5.65)$.

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 2, Problem 66

Instant Answer

Solved by Expert Carson Merrill

07/06/2021

Step 1

We can express this as a function of $x$ by converting the percentage to a decimal. $6\%$ is equivalent to $0.06$ in decimal form. Therefore, the function $T(x)$ is given by: \[T(x) = 0.06x\] Show more…

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Sales Taxes In a certain state, the sales tax $T$ on the amount of taxable goods is $6 \%$ of the value of the goods purchased $x$, where both $T$ and $x$ are measured in dollars. a. Express $T$ as a function of $x$. b. Find $T(200)$ and $T(5.65)$.

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Key Concepts

Linear Functions

A linear function is one in which the dependent variable changes at a constant rate with respect to the independent variable. In this context, the tax relationship is expressed as a linear function T(x) = 0.06x, representing a direct proportionality between the taxable amount and the sales tax applied.

Function Evaluation

Function evaluation is the process of substituting a given input value into a function to calculate the corresponding output. This technique is used to find specific instances of the function, such as computing T(200) and T(5.65) by substituting these values into the defined linear function.

Percentage Calculations

This concept involves converting a percentage into a decimal form to apply it in mathematical operations. For example, understanding that 6% can be expressed as 0.06 is essential for correctly determining proportions of any given quantity.

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