Jamie is starting a new marketing strategy that causes her

Question

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 \(50 \cdot 2^6 = 3200\).