Advanced Math - Set - 7 | SAT Math Section

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Mar 23, 2024

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$$f(t)=8,000(0.65)^{t}$$The given function $f$ models the number of coupons a company sent to their customers at the end of each year, where $t$ represents the number of years since the end of 1998, and $0\leq t\leq 5$. If $y=f(t)$ is graphed in the $ty$-plane, which of the following is the best interpretation of the $y$-intercept of the graph in this context?

Difficulty: Hard

The minimum estimated number of coupons the company sent to their customers during the 5 years was 1,428.

The minimum estimated number of coupons the company sent to their customers during the 5 years was 8,000.

The estimated number of coupons the company sent to their customers at the end of 1998 was 1,428.

The estimated number of coupons the company sent to their customers at the end of 1998 was 8,000.

If $u-3=\frac{6}{t-2}$, what is $t$ in terms of $u$?

Difficulty: Hard

t=\frac{1}{u}

t=\frac{2u+9}{u}

t=\frac{1}{u-3}

t=\frac{2u}{u-3}

$$-9x^{2}+30x+c=0$$In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

Difficulty: Hard

3

0

$-25$

$-53$

$$\frac{x^{2}}{\sqrt{x^{2}-c^{2}}}=\frac{c^{2}}{\sqrt{x^{2}-c^{2}}}+39$$In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?

Difficulty: Hard

$-c$

-c^{2}-39^{2}

-\sqrt{39^{2}-c^{2}}

-\sqrt{c^{2}+39^{2}}

$f(x)=2(3^{x})$For the function $f$ defined above, what is the value of $f(2)$?

Difficulty: Easy

$9$

$12$

$18$

$36$

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