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You are here: Home / ACT Released Tests / Video Explanations: 2020 December ACT (D03)

Video Explanations: 2020 December ACT (D03)

2020 December ACT (D03): Answers

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The video playlist below organizes explanations to all of the mathematics questions in the 2020 December ACT test(Form code D03).

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Comments

  1. Anthony Ryan says

    February 25, 2021 at 12:12 PM

    Re Question 29. why do you plug in a 100 for x and then multiply again by 100.
    How does plugging in a 100 give you the price per pound when you could plug in nearly any number and get the same price per pound?
    Thank you!!

    Reply
    • Dabral says

      March 31, 2021 at 9:41 AM

      Hi Anthony,

      Kathy has already answered your question, but let me elaborate a bit more.

      The price function only gives a value of $3.50$, when $x$ is fairly large. So you are right that if $x$ was $50$ or $100$, the price would be nearly the same. But that is not the case when $x$ is say equal to $1$ or $2$.

      The price per pound of the raisin-nut mixture depends on the pounds that one would purchase. If we were purchasing $2$ lbs, then we would need to first find the price per pound, which in this case would be equal to $3.50 +(0.9)^2 = 4.31$ per pound, the total price would be the pounds purchased ($2$ pounds here) multiplied by the price per pound of $4.31$, which would be $8.62$. The price function is exponential, and as $x$ gets large the price rapidly approaches $3.50$.

      Dabral

      Reply
  2. Kate Dalby says

    March 31, 2021 at 7:46 AM

    Thank you for your question. I didn’t understand the problem until I read your question.

    If you were buying just one pound, you would pay $\$4.40$. IE. $\$3.50 + .90^1$/pound.

    If you bought 100 lbs, your per pound cost would be $\$3.50 + .90^100$/pound IE $\$3.50$ + virtual nothing extra/lb. Therefore 100 pounds would be $\$350$.

    Thank you for asking this.

    Reply

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