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)
Jamie substituted m = 6 into the
expression 6.250
= 3200.
Jamie substituted m = 6 into the
expression 50.6² = 1800.
Jamie substituted m = 6 into the
expression 50.26 = 3200.
Jamie substituted m = = 6 into the
expression 50·2·6
=
600.

Answer 1

To determine how Jamie reached the solution of 3,200 clients after 6 months using the expression \(50 \cdot 2^m\), we need to substitute \(m = 6\) into the expression.

Let's break down the expression:

1. The expression for the number of clients after \(m\) months is given by:
\[
\text{Clients} = 50 \cdot 2^m
\]

2. If we substitute \(m = 6\):
\[
\text{Clients} = 50 \cdot 2^6
\]

3. We know that \(2^6 = 64\):
\[
\text{Clients} = 50 \cdot 64
\]

4. Calculating this gives:
\[
\text{Clients} = 50 \cdot 64 = 3200
\]

Now, looking at the options provided:

- **Option 1**: Jamie substituted \(m = 6\) into the expression \(6.250 = 3200\). (Incorrect)
- **Option 2**: Jamie substituted \(m = 6\) into the expression \(50 \cdot 6^2 = 1800\). (Incorrect)
- **Option 3**: Jamie substituted \(m = 6\) into the expression \(50 \cdot 2^6 = 3200\). (Correct)
- **Option 4**: Jamie substituted \(m = 6\) into the expression \(50 \cdot 2 \cdot 6 = 600\). (Incorrect)

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