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

Anthony Ryansays

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!!

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 $3.50$.

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 $\$350$.

Anthony Ryan says

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!!

Dabral says

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

Kate Dalby says

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.