Samantha wants to work on her herb garden. She decides to start with a basil plant that is 3 inches tall. The plant doubles in height each week. The exponential expression that models this scenario is 3⋅2w

Question

, where w
represents the number of weeks Samantha cares for the plant.

Samantha wants to know how tall the basil plant will be in 4 weeks. According to her calculations, the basil plant will be 48 inches tall. How did Samantha reach this answer?

(1 point)
Responses

Samantha substituted in 4 for w
and found 3⋅24=48
.
Samantha substituted in 4 for w and found 3 times 2 to the 4th power is equal to 48.

Samantha substituted in 4 for w
and found 3⋅2⋅4=48
.
Samantha substituted in 4 for w and found 3 times 2 times 4 is equal to 48.

Samantha guessed based on her own height that the basil plant was about 48 inches tall.
Samantha guessed based on her own height that the basil plant was about 48 inches tall.

Samantha compared the basil plant to others in her herb garden to approximate the height.

Answer 1

Samantha substituted in 4 for w and found 3 times 2 to the 4th power is equal to 48.

This is how her calculations would look:

1. Substitute \(w = 4\) into the expression: \(3 \cdot 2^w = 3 \cdot 2^4\).
2. Calculate \(2^4 = 16\).
3. Then calculate \(3 \cdot 16 = 48\).

So indeed, the basil plant would be 48 inches tall after 4 weeks.