A proposed energy tax T on gasoline, which would affect the cost of driving a vehicle, is to be computed by multiplying the number x of gallons of gasoline by 125,000 (the number of BTUs per gallon) and then multiplying the total BTUs by the tax ($0.342 per 1,000,000 BTUs). Find a linear function for T in terms of x .
for this question the answer I got was:
T(x) = x*125000 * 0.342/1000000
Edit: The instructor gave no answer, its a practice problem , I don't know if its right.
No, it is wrong. Here's why:
The tax is charged by $\frac{0.342}{1,000,000}\frac{$}{BTUs}$. Since each gallons have $125000$ BTUs, it's $\frac{1}{4}$ of the tax charged over $1,000,000$ BTUs (I'm doing $\frac{125,000}{1,000,000}$). In other words, we have to compute the function $T: x \rightarrow $$ as such:
$T(x) = 125,000x*\frac{0,342}{8} \Leftrightarrow T(x) = 15,625x*0,342 \Leftrightarrow T(x) = 5,343.75x$, where $x$ is the number of gallons.