Question #f1c81b3b - SAT Suite Question Bank

ID: f1c81b3b

Modded SAT Question Bank by Abdullah Mallik

The exponential function $g$ is defined by $g left parenthesis x right parenthesis equals 19 dot a Superscript x$ , where $a$ is a positive constant. If $g left parenthesis 3 right parenthesis equals 2,375$ , what is the value of $g left parenthesis 4 right parenthesis$ ?

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Correct Answer: 11875

Rationale

The correct answer is $11,875$ . It's given that the exponential function $g$ is defined by $g left parenthesis x right parenthesis equals 19 dot a Superscript x$ , where $a$ is a positive constant, and $g left parenthesis 3 right parenthesis equals 2,375$ . It follows that when $x equals 3$ , $g left parenthesis x right parenthesis equals 2,375$ . Substituting $3$ for $x$ and $2,375$ for $g (x)$ in the given equation yields $2,375 equals 19 dot a cubed$ . Dividing each side of this equation by $19$ yields $125 equals a cubed$ . Taking the cube root of both sides of this equation gives $a equals 5$ . Substituting $4$ for $x$ and $5$ for $a$ in the equation $g left parenthesis x right parenthesis equals 19 dot a Superscript x$ yields $g left parenthesis 4 right parenthesis equals 19 dot 5 Superscript 4$ , or $g left parenthesis 4 right parenthesis equals 11 comma 875$ . Therefore, the value of $g left parenthesis 4 right parenthesis$ is $11,875$ .

Question Difficulty: Medium