Question

Tom owns 150 baseball cards. Every year his collection grows by 4%. What is the formula to determine the number of baseball cards in Tom’s collection after n years?A. an=150(1.04)n+1B. an=150(0.04)nC. an=150(1.04)nD. an=150(0.04)n−1

Answer 1

First, let's visualize the number of baseball cards Tom has every year.

Beginning = 150 cards

After 1 year = 150 + 150 (4%) = 150 (1 + 4%) = 156 cards

After 2nd year = 156 (1 + 4%) = 162.24 cards

After 3rd year = 162.24 (1 + 4%) = 168.7296 cards

After 4th year = 168.7296 (1 + 4%) = 175.479 cards

From this, we can see that the formula to get the number of cards in "n" years is this:

1. 1 year: 150(1.04) = 156 cards

2. 2nd year: [(150)(1.04)][1.04] = 162.24 cards

3. 3rd year: {[(150)(1.04)][1.04]}{1.04} = 168.7296 cards

or in general, the formula is:

`a_n=150(1.04)^n`

where "n" is the number of years. The answer is Option C.