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⋅2^m 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?

Question

A) Jamie substituted m = 6 into the expression 50 ⋅ 2 ⋅ 6 = 600.
B) Jamie substituted m = 6 into the expression 6 ⋅ 2^50 = 3200.
C) Jamie substituted m = 6 into the expression 50 ⋅ 2^6 = 1800.
D) Jamie substituted m = 6 into the expression 50 ⋅ 2^6 = 3200.

Answer 1

To determine how Jamie arrived at the conclusion that she had 3,200 clients after 6 months, we can analyze the expression provided: \(50 \cdot 2^m\).

Here, \(m\) represents the number of months. If we substitute \(m = 6\) into the expression, we calculate:

\[ 50 \cdot 2^6 \]

First, we need to compute \(2^6\):

\[ 2^6 = 64 \]

Now, we multiply that by 50:

\[ 50 \cdot 64 = 3200 \]

Since we arrived at 3,200 clients after substituting \(m = 6\) into the expression, it means the correct statement is:

D) Jamie substituted m = 6 into the expression \(50 \cdot 2^6 = 3200\).