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Advanced Math / Nonlinear functions Difficulty: Medium

$x$ $x$	$y$ $y$
$1$ $1$	$11$ $11$
$2$ $2$	$19$ $19$
$3$ $3$	$a$ $a$

The table shows three values of $x$ and their corresponding values of $y$ for the equation $y = 4 {(2)}^{x} + 3$ . In the table, $a$ is a constant. What is the value of $a$ ?

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Explanation

Choice B is correct. It's given that the table shows three values of $x$ and their corresponding values of $y$ for the equation $y = 4 {(2)}^{x} + 3$ . It's also given that when $x equals 3$ the corresponding value of $y$ is $a$ , and $a$ is a constant. Substituting $3$ for $x$ and $a$ for $y$ in the given equation yields $a = 4 {(2)}^{3} + 3$ , or $a equals 35$ . Therefore, the value of $a$ is $35$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.