Answer: No.
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In the figure attached, "Answer choice: # [3], which is:
"$13,287.46 ", is INCORRECT. The correct answer is:
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Answer choice #[1]: " $2,932 .24 " .
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{NOT: "Answer choice: #[3]: "$13,287. 46 ".}.
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Explanation:
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For "Number 11" (in the figure attached):
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Given: " v(x) = (28,000)(0.78)ˣ " ;
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To get the answer:
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The question asks: "How much MORE is Glen's car worth AFTER 3 (THREE) YEARS than AFTER 4 (FOUR) YEARS"?
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→Note well: The car is worth MORE after THREE (3) years than after FOUR (4) YEARS. Does this makes sense? Yes! (
→ (Concept known as "devaluation"; or, "depreciation").
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Also, look at the entire function:
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Given: v(x) = (28,000)(0.78)ˣ ;
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Since this involves a "fraction" less than one, raise to an exponent, does it make sense that "v(x)" will be a greater value when "x = 3" (i.e. "3 years") than when "x = 4" (i.e. "4 years")? Yes!
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So, to get our answer:
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We subtract:
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"(28,000)(0.78)⁴ " (the lower value).
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FROM:
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"(28,000)(0.78)³ " (the higher value).
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Let us let: "(28,000)" = x ;
and let: (0.78) = y ;
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xy³ − xy⁴ =
xy³(1 − y) =
(28,000)*(0.78)³ * [(1− (0.78)] =
(28,000)*(0.474552)*(0.22) =
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$ 2923.24032 ; which corresponds with:
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Answer choice #[1]: $2,932.24 .
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{NOT: "Answer choice: #[3]: "$13,287.46" }.
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