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# SAT Functions as Models

$\begin{array}{|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1\\ \hline g(x) & \frac{9}{4} & \frac{9}{2} & 9 & 18\\ \hline \end{array}$

The table above shows some values of the function $$g(x)=ba^{x}.$$ If $$a$$ and $$b$$ are nonnegative constants, what is the value of $$a$$?

(A) $$\ \ \frac{1}{4}$$
(B) $$\ \ \frac{1}{2}$$
(C) $$\ \ 1$$
(D) $$\ \ 2$$
(E) $$\ \ 9$$

An experimental population of $$100$$ fruit flies increases each hour by $$4\%$$. If the approximate number of fruit flies is given by the function $$Q(t)=100x^{t}$$, where $$t$$ is measured in hours, what is the value of $$x$$?

(A) $$\ \ 0.04$$
(B) $$\ \ 0.6$$
(C) $$\ \ 1.04$$
(D) $$\ \ 1.6$$
(E) $$\ \ 4$$

A stone thrown upward from the top of a building misses the edge of the building on its way down. Its height can be found using the equation

$y=y_{0}+v_{0}t+\frac{1}{2}at^{2},$

where $$y_{0}$$ is the original position of the stone, $$v_{0}$$ is its initial velocity, $$a$$ is the acceleration due to gravity, and $$t$$ is the time the stone spends in the air. At what time does the stone return to its original height, if $$y_{0}=0$$ m, $$v_{0}=25$$ m/s, and the acceleration due to gravity is $$-10$$ m/s$$^{2}$$.

(A) $$\ \ 3$$ s
(B) $$\ \ 5$$ s
(C) $$\ \ 7$$ s
(D) $$\ \ 9$$ s
(E) $$\ \ 11$$ s

$$^{63}\text{Ni}$$, a radioisotope of nickel, has a half-life of $$100$$ years. If the quantity of $$^{63}\text{Ni}$$ present (in grams) after $$x$$ years is given by the function $$y(x)=10\left(\frac{1}{2}\right)^{\frac{x}{100}}$$, how much of the initial mass is present after $$80$$ years?

(A) $$\ \ 0.80$$ g
(B) $$\ \ 1.00$$ g
(C) $$\ \ 3.62$$ g
(D) $$\ \ 5.74$$ g
(E) $$\ \ 80.00$$ g

A family-owned juice business has a daily production cost of $$C(x)=5000 - 12x + 2x^{2}$$ where $$C$$ is the total cost in dollars and $$x$$ is the number of juice crates produced. How much greater is the cost of production for $$18$$ crates than the cost of production for $$10$$ crates?

(A) $$\ \ 352$$
(B) $$\ \ 5032$$
(C) $$\ \ 5432$$
(D) $$\ \ 6232$$
(E) $$\ \ 10512$$

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