Jamie is starting a new marketing strategy that causes her number of clients to grow exponentially. Jamie starts with 50 clients, and each month, her number of clients doubles. The expression 50 x 2^m can be used to model the expression. Jamie found that after just 6 months, she had reached 3,200 clients. How did Jamie reach this solution?

Answer 1

To solve for the number of clients Jamie has after 6 months using the given expression \(50 \times 2^m\), we can substitute \(m\) with 6, since she is looking at the scenario after 6 months.

1. Formula: The expression given is: \[ \text{Number of clients} = 50 \times 2^m \]

2. Substituting \(m = 6\): \[ \text{Number of clients} = 50 \times 2^6 \]

3. Calculating \(2^6\): \[ 2^6 = 64 \]

4. Calculating the total number of clients: \[ \text{Number of clients} = 50 \times 64 = 3200 \]

Thus, using the expression \(50 \times 2^m\), when \(m = 6\), Jamie calculates that she will have 3200 clients after 6 months. This matches her observation, confirming that she reached 3200 clients through exponential growth, starting from 50 clients and doubling each month.