<p>The number of baseball cards in caleb's collection doubles every three months. If after 9 months he has b baseball cards, then which of the following is an expression for the number of baseball cards in his collection after y years? </p>
<p>1)(2^y)b
2)(2^4y-3)b
3)(2^4y)b
4) 2b^(4y-3)
5)( 2^y)b^y+2</p>
<p>Answer is 2)
can someone explain? Idk why I don't understand it.</p>
<p>For sure this is a tricky problem. But I think I get it. </p>
<p>We see, obviously, that 3 months is 1/4 of a year.
As such, 2^4y is an expression for how much the amount of cards has changed over time.</p>
<p>Let’s say x is the amount of cards in the beginning.
x*2^4y = b if y=3/4</p>
<p>So b = 8x and therefore x = b/8</p>
<p>Now we’re trying to find an expression that relates his overall collection to years. This will require x, but as we can see, x, or any other placeholder variable isn’t found in the answers. As such, we need to use b for this.</p>
<p>(b/8)2^4y</p>
<p>As 2^3 = 8, we can use the 2^4y to get rid of the 1/8 coefficient. Subtracting 3 from the exponent of a base of 2 is the same as dividing by 8.</p>
<p>b(2^4y-3)</p>
<p>By no means an easy problem, this one took me a good 10 minutes, and I got an 800 on my math section. Is this official blue book?</p>
<p>I think it’s pretty simple. </p>
<p>So you know that after 9 months, Caleb has b baseball cards so that means however many years you get in the end, u subtract 3 (months) from it. </p>
<p>So for starters, it is “2” for the doubling of however many years to the power of however many years which is “y” multiplied by 4 because it is stated that every 3 months, his cards are doubled. You put all of this together and multiply it by “b” because that’s the number of baseball cards he will have in “y” years.</p>
<p>In the end, the equation should be answer (2) which is (2^4y-3)b</p>
<p>Ic… Ugh I hate math lol this is from the Princeton review bk btw</p>
<p>Yeah, that explains the difficulty, lol. Also, I want to say that Dre’s explanation is wrong for subtracting 3.</p>
<p>isnt correct since there are b baseball cards after 9months? so then it would be 4y-3?</p>
<p>i wrote how many he would have in january first year (2), in october first year (b=32) and in january third year (y=2) and just pluged in the numbers, about 5 minutes of work. is this question considered a level 5 (the hardest) ?</p>
<p>Guessing and checking (aka ProjectAmericas way) is probably the fastest on this kind of problem. On the math sat (1/2) they don’t care how you got your answer, just whether its correct or not. Since you’re given a calculator, I’d just guess and check for this problem. But I mean, if you can quickly solve it that way, that’s helpful to check your work, or the other way around. Whichever works best.</p>