The table shows three values of and their corresponding values of for the equation . | | | |---|---| | 1 | 11 | | 2 | 19 | | 3 | | In the table, is a constant. What is the value of ?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 29 | Free SAT Prep | Aniko

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Question 29·Medium·Nonlinear Functions

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The table shows three values of $x$ and their corresponding values of $y$ for the equation $y = 4(2)^x + 3$ .

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

In the table, $a$ is a constant. What is the value of $a$ ?

For exponential function tables, always go straight to substitution: plug the given $x$ into the function, simplify the exponent first, then multiply and add in the correct order. Use the table entries you’re given (like checking $x=1$ or $x=2$ ) to confirm you understand how the function is applied, and watch for common traps such as forgetting constant terms (like +3) or misreading which $x$ -value the question is asking about.

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Use the given formula

The $y$ -values in the table all come from the equation $y = 4(2)^x + 3$ . How did they get 11 when $x=1$ and 19 when $x=2$ ?

Apply the same process to $x=3$

Write the equation with $x=3$ : replace $x$ by 3 in $y = 4(2)^x + 3$ . What expression do you get?

Simplify in the right order

Evaluate the exponent $2^3$ first, then multiply by 4, and finally add 3. Be careful not to forget the +3 at the end.

Desmos Guide

Evaluate the function at $x=3$ in Desmos

In Desmos, type the function y = 4*2^x + 3. Then either use the table feature (click the gear icon next to the expression and select "Table") or type x = 3 on a new line and tap the point where it intersects the graph. Read off the corresponding $y$ -value when $x=3$ ; that is the value of $a$ .

Step-by-step Explanation

Understand how the table is made

The table is built using the equation $y = 4(2)^x + 3$ .

For each row, you plug the $x$ -value into the equation to get the corresponding $y$ -value.
For example, when $x=1$ :

y = 4(2)^1 + 3 = 4 \cdot 2 + 3 = 8 + 3 = 11

which matches the table. The same idea is used to find $a$ when $x=3$ .

Substitute $x=3$ into the equation

Now use the same equation for $x=3$ .

Plug $x=3$ into $y = 4(2)^x + 3$ :

y = 4(2)^3 + 3

Your job is to simplify this expression step by step.

Simplify the expression to find $a$

First evaluate the exponent:

2^3 = 8

Then substitute this back into the expression:

y = 4 \cdot 8 + 3 = 32 + 3 = 35

So, when $x=3$ , $y=35$ , which means $a = 35$ . The correct answer is B) 35.

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Step-by-step Explanation

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Step-by-step Explanation