To determine how Jamie reached her solution, let's analyze the given expression and options.
The expression given is \( 50 \cdot 2^m \), where \( m \) represents the number of months. Jamie starts with 50 clients, and her number of clients doubles each month.
To find the number of clients after 6 months, we set \( m = 6 \):
\[ \text{Number of clients} = 50 \cdot 2^6 \]
Now, we calculate \( 2^6 \):
\[ 2^6 = 64 \]
Next, we multiply this by 50:
\[ 50 \cdot 64 = 3200 \]
So, after substituting \( m = 6 \) into \( 50 \cdot 2^m \), Jamie indeed finds that she has 3200 clients after 6 months.
Now, let's review the provided options:
A) Jamie substituted \( m=6 \) into the expression \( 50 \cdot 2 \cdot 6 = 600 \).
- This is incorrect; this does not use the correct formula.
B) Jamie substituted \( m=6 \) into the expression \( 6 \cdot 2^{50} = 3200 \).
- This is incorrect; it uses the wrong formula (and \( 2^{50} \) is much larger than required).
C) Jamie substituted \( m=6 \) into the expression \( 50 \cdot 2^6 = 1800 \).
- This is incorrect; \( 50 \cdot 2^6 \) equals 3200, not 1800.
D) Jamie substituted \( m=6 \) into the expression \( 50 \cdot 2^6 = 3200 \).
- This is correct, as it matches our calculations.
The correct answer is:
D) Jamie substituted m = 6 into the expression 50 ⋅ 2^6 = 3200.
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