Question

Drag and drop the expressions into the correct locations.

Perry buys a bag of 20 carrots on the first day. The second day, he eats half of the bag. Each day after, he eats half of what is left in the bag. Create a sequence formula that describes the number of carrots Perry will have on any given day.

(1 point)

Answer 1

To create a sequence formula that describes the number of carrots Perry will have on any given day, we can define the number of carrots left after each day as follows:

Let \( C(n) \) be the number of carrots remaining after \( n \) days.

- On the first day (when \( n = 0 \)), Perry buys 20 carrots:
\[
C(0) = 20
\]

- On the second day (when \( n = 1 \)), he eats half:
\[
C(1) = C(0) \times \frac{1}{2} = 20 \times \frac{1}{2} = 10
\]

- On the third day (when \( n = 2 \)), he eats half of what is left:
\[
C(2) = C(1) \times \frac{1}{2} = 10 \times \frac{1}{2} = 5
\]

- On the fourth day (when \( n = 3 \)):
\[
C(3) = C(2) \times \frac{1}{2} = 5 \times \frac{1}{2} = 2.5
\]

From this pattern, we can see that each day he has half of what he had the previous day. Therefore, the sequence can be summarized by the formula:

\[
C(n) = 20 \times \left( \frac{1}{2} \right)^{n}
\]

Where \( n \) is the number of days after the first day (starting from 0).

So the completed drag and drop would look like:
- \( C(0) = 20 \)
- \( C(n) = 20 \times \left( \frac{1}{2} \right)^{n} \)

This formula describes the number of carrots Perry will have on any given day \( n \).