Question

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) Responses Jamie substituted m=6 into the expression 50⋅2⋅6=600 . Jamie substituted m is equal to 6 into the expression 50 times 2 times 6 is equal to 600. Jamie substituted m=6 into the expression 50⋅26=3200 . Jamie substituted m is equal to 6 into the expression 50 times 2 to the 6th power is equal to 3200. Jamie substituted m=6 into the expression 6⋅250=3200 . Jamie substituted m is equal to 6 into the expression 6 times 2 to the 50th power is equal to 3200. Jamie substituted m=6 into the expression 50⋅62=1800 .

Answer 1

To find out how Jamie reached the solution of having 3,200 clients after 6 months, we can refer to the expression \( 50 \cdot 2^m \), where \( m \) represents the number of months.

1. **Initial Setup**: Jamie starts with 50 clients.
2. **Doubling Each Month**: Each month, the number of clients doubles, which is modeled by multiplying by \( 2^m \).
3. **Calculating for 6 Months**: We substitute \( m = 6 \) into the expression.

The expression becomes:
\[
50 \cdot 2^6
\]

Now, we need to calculate \( 2^6 \):
\[
2^6 = 64
\]

Next, we multiply this by the initial number of clients (50):
\[
50 \cdot 64 = 3200
\]

Thus, after substituting \( m = 6 \) into the expression, Jamie calculated:
\[
50 \cdot 2^6 = 3200
\]

The correct response is: **Jamie substituted \( m = 6 \) into the expression \( 50 \cdot 2^6 = 3200 \).**