The function C(x) = 0.06x + 18 gives a household's monthly... | SAT Linear functions Question, Answer Explained

Math · AlgebraHard

The function $C(x) = 0.06x + 18$ gives a household's monthly electricity cost, in dollars, for using $x$ kilowatt-hours of electricity. Which function $M$ gives the monthly cost, in dollars, for using $y$ megawatt-hours of electricity? ( $1$ megawatt-hour $= 1{,}000$ kilowatt-hours)

$M(y) = 0.00006y + 18$

$M(y) = 0.06y + 0.018$

$M(y) = 60y + 18$

$M(y) = 60y + 18{,}000$

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Answer: C

Using $y$ megawatt-hours means using $x = 1{,}000y$ kilowatt-hours. Substitute: $M(y) = 0.06(1{,}000y) + 18 = 60y + 18$ . The fixed charge of $\$18$ doesn't depend on usage, so it doesn't change.

Choice A divides $0.06$ by $1{,}000$ , but each megawatt-hour costs $1{,}000$ times as much as each kilowatt-hour, not less.

Why the other choices are wrong

A. This divides the rate by 1,000. A megawatt-hour is 1,000 kilowatt-hours, so it costs 1,000 times as much.
B. This keeps the per-unit rate and divides the fixed charge by 1,000. The rate should be multiplied by 1,000, and the fixed charge stays $18.
D. This multiplies the fixed $18 charge by 1,000, but that charge doesn't depend on how much electricity is used.

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