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⋅2m 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? (1 point)

To understand how Jamie reached the solution regarding her client growth, let's analyze the exponential growth model she is using, expressed as:

\[ C(m) = 50 \cdot 2^m \]

Where:
- \( C(m) \) is the number of clients after \( m \) months,
- \( 50 \) is the initial number of clients,
- \( 2^m \) represents the doubling of clients each month.

Now, if we want to find out how many clients Jamie has after 6 months, we will plug \( m = 6 \) into the equation:

\[ C(6) = 50 \cdot 2^6 \]

Calculating \( 2^6 \):

\[ 2^6 = 64 \]

Now substituting back into the equation:

\[ C(6) = 50 \cdot 64 \]

Now we perform the multiplication:

\[ C(6) = 3200 \]

This means that after 6 months, the number of clients Jamie has is indeed 3200, confirming that her expression and calculations are accurate. Thus, Jamie concludes that she reached 3200 clients through the quantitative growth determined by her doubling strategy each month.