Advanced Math - Set - 13 | SAT Math Section

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Mar 23, 2024

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$$f(x)=9(4)^{x}$$The function $f$ is defined by the given equation. If $g(x)=f(x+2)$, which of the following equations defines the function $g$?

Difficulty: Hard

g(x)=18(4)^{x}

g(x)=144(4)^{x}

g(x)=18(8)^{x}

g(x)=81(16)^{x}

If a and c are positive numbers, which of the following is equivalent to $\sqrt{(a+c)^{3}}\cdot\sqrt{a+c}$?

Difficulty: Hard

$a+c$

a^{2}+c^{2}

a^{2}+2ac+c^{2}

a^{2}c^{2}

The total revenue from sales of a product can be calculated using the formula $T=PQ$, where $T$ is the total revenue, $P$ is the price of the product, and $Q$ is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of $P$ and $T$?

Difficulty: Easy

Q=\dfrac{P}{T}

Q=\dfrac{T}{P}

$Q=PT$

$Q=T-P$

The function $f$ is defined by $f(x)=x^{3}+15$. What is the value of $f(2)$?

Difficulty: Easy

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Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (${}^{\circ}$F). The temperature of the hot chocolate was 185${}^{\circ}$F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156${}^{\circ}$F at 6:05 p.m. and 135${}^{\circ}$F at 6:10 p.m. The hot chocolate's temperature continued to decrease. Of the following functions, which best models the temperature $T(m)$, in degrees Fahrenheit, of Kao's hot chocolate $m$ minutes after it started cooling?

Difficulty: Hard

T(m)=185(1.25)^{m}

T(m)=185(0.85)^{m}

T(m)=(185-70)(0.75)^{\frac{m}{5}}

T(m)=70+115(0.75)^{\frac{m}{5}}

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