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

Question

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⋅2^6=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⋅2^50=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⋅6^2=1800
.
Jamie substituted m is equal to 6 into the expression 50 times 6 squared is equal to 1800.
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Answer 1

The correct response is:

Jamie substituted m=6 into the expression 50⋅2^6=3200. Jamie substituted m is equal to 6 into the expression 50 times 2 to the 6th power is equal to 3200.

Here's the reasoning behind this choice:

To find the number of clients after 6 months, Jamie uses the expression that models her client growth: \( 50 \cdot 2^m \). By substituting \( m = 6 \):

\[ 50 \cdot 2^6 = 50 \cdot 64 = 3200. \]

This shows that after 6 months, she has indeed reached 3200 clients. Other options provided do not correctly substitute into the model or do not reflect the exponential growth being modeled.