<p>I always suck at these problems for some reason and the Collegeboard explanation fails so I can't really understand why the answer is B. Help please?</p>
<p>All you need to do is substitute a number for n.</p>
<p>Let’s call n=1.
Therefore, 2^(n+1) + 2^(1) = k
4+2=k
and then 4+2=6
k=6</p>
<p>Now, substitute the same n in for 2^(n+2)
2^(1+2)=2^(3)=8</p>
<p>now say 6 x ‘what’ is equal to 8</p>
<p>The answer is 4/3 or B.</p>
<p>2^n means you repeat the multiplication of 2 by itself n times. 2^(n+1) is the same exponent except you multiply by 2 one more time.</p>
<p>so 2^(n+1) is the same as 2 times 2^n, or 2<em>(2^n)
2^(n+2) is the same as 2 times 2 times 2^n, or 4</em>(2^n)</p>
<p>2^n + 2^(n+1) = k
1(2^n) + 2(2^n) = k
3(2^n)* = k</p>
<p>2^(n+2) = 4(2^n)*</p>
<p>4<em>(2^n) in terms of k is (4/3)k because it is 4/3 times k, or 4/3 times 3</em>(2^n)</p>
<p>the key to solving this problem is knowing how to break down the exponents so that you can combine terms with the same exponent to solve</p>