<p>The number of baseball cards in Caleb's collection doubles every three months. If after 9 months he has 'b' baseball cards, then an expression for the number of baseball cards in his collection after 'y' years is given by</p>
<p>A) 2^y<em>b
B) 2^(4y-3)</em>b
C) 2^(4y)<em>b
D) 2</em>b^(4y-3)
E) 2^(y)*b^(y+2)</p>
<p>The answer is B, but I don't still get it. HELPHELP</p>
<p>Here’s a pretty efficient way to do this.</p>
<p>Let’s assume that initially, Caleb has 1 baseball card (at t = 0 months).
t = 3 he has 2
t = 6 he has 4
t = 9 he has 8
t = 12 he has 16
t = 15 he has 32
t = 18 he has 64
t = 21 he has 128
t = 24 he has 256</p>
<p>So our ‘b’ for this problem is 8 (the number of cards at t = 9). Let’s let y = 2 (after 24 months, when he has 256 cards). Now let’s plug 8 in for b, 2 in for y, and see what expression gives us 256.</p>
<p>A) 32 - wrong
B) 256
C) 2048 - wrong
D) 65536 - wrong
E) 16384 - wrong</p>
<p>B is correct</p>
<p>This is perfect time to just pick numbers and see the results.
For example, at 9 months let him have 10 cards. Since it doubles every 3 months, at 12 months/1 year he will have 20 cards.
At 2 years, he will have 320 cards.</p>
<p>So for the variables the problem specifies, b=10 y=2 and we are trying to get the answer of 320! Now lets plug in our variables to the choices. Note: We found 2 years rather than 1 to eliminate the possibility of 2 matches.</p>
<p>A: 2^y<em>b=2^2</em>10=4<em>10=40 NO!
B: 2^(4y-3)</em>b=2^5<em>10=32</em>10- 320 YES! </p>
<p>The correct answer is B!</p>