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

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⋅62=1800
.
Jamie substituted m is equal to 6 into the expression 50 times 6 squared is equal to 1800.

Jamie substituted m=6
into the expression 50⋅26=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 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 6⋅250=3200
.
Jamie substituted m is equal to 6 into the expression 6 times 2 to the 50th power is equal to 3200.

Answer 1

To determine how Jamie reached the solution of 3,200 clients after 6 months, we need to closely examine the growth formula and the provided response options.

The expression used to model the number of clients is \( 50 \cdot 2^m \). In this case, \( m \) represents the number of months.

If Jamie wants to find the number of clients after 6 months, she would substitute \( m = 6 \) into the expression:

\[ 50 \cdot 2^6 \]

Calculating \( 2^6 \):

\[ 2^6 = 64 \]

Now, substituting this value back into the expression:

\[ 50 \cdot 64 = 3200 \]

Thus, after evaluating this expression, Jamie finds that after 6 months, she has 3,200 clients.

Therefore, 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.