Question 114·Medium·Math

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

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

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 $a$.

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 $x=1$:

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

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

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

Your job is to simplify this expression step by step.

First evaluate the exponent:

Then substitute this back into the expression:

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