QuestionFind a linear function for the energy tax $T$ on gasoline in terms of the number of gallons $x$ : $T = 0.04275 x$ .

Studdy Solution

STEP 1

Assumptions1. The number of gallons of gasoline bought is represented by $x$ . Each gallon of gasoline has125,000 BTUs3. The tax rate is34. cents per million BTUs4. The tax $is calculated by multiplying the total BTUs by the tax rate5. We need to find a linear function for$ in terms of $x$

STEP 2

First, we need to find the total BTUs for the number of gallons of gasoline bought. We can do this by multiplying the number of gallons by the number of BTUs per gallon.
$Total\, BTUs = Number\, of\, gallons \times BTUs\, per\, gallon$

STEP 3

Now, plug in the given values for the number of gallons and BTUs per gallon to calculate the total BTUs.
$Total\, BTUs = x \times125,000$

STEP 4

Now that we have the total BTUs, we can calculate the tax $$ by multiplying the total BTUs by the tax rate. However, since the tax rate is given per million BTUs, we need to convert the total BTUs to millions of BTUs.
$Total\, BTUs\, in\, millions = Total\, BTUs /1,000,000$

STEP 5

Plug in the value for the total BTUs to calculate the total BTUs in millions.
$Total\, BTUs\, in\, millions = x \times125,000 /1,000,000$

STEP 6

Now, calculate the tax $$ by multiplying the total BTUs in millions by the tax rate.
$= Total\, BTUs\, in\, millions \times Tax\, rate$

STEP 7

Plug in the values for the total BTUs in millions and the tax rate to calculate the tax $$.
$= x \times125,000 /1,000,000 \times34.2$

STEP 8

Now, simplify the equation to find the linear function for $$ in terms of $x$.
$=0.04275x$ So, the linear function for $$ in terms of $x$ is $ =0.04275x$.

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