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Question

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)
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Response container 1 Coefficient of the sequence formula ⋅
Response container 2 Exponential factor of the sequence formula

Answer 1

To create a sequence formula that describes the number of carrots Perry will have on any given day, we'll start by understanding the situation:

• On the first day (day 0), Perry starts with 20 carrots.
• On the second day (day 1), he eats half of what he has: \(20 / 2 = 10\) carrots remaining.
• On the third day (day 2), he eats half again: \(10 / 2 = 5\) carrots remaining.
• On the fourth day (day 3), he eats half again: \(5 / 2 = 2.5\) carrots remaining.

From this pattern, we can see that each day he is left with half of what he had the previous day. This can be established in a formula format.

Considering \(a_n\) to be the number of carrots left on day \(n\):

1. Coefficient of the sequence formula: The starting amount of carrots, which is 20.
2. Exponential factor of the sequence formula: Each day represents a half of the previous day, which can be expressed as \( (1/2)^n \).

So, the sequence formula can be written as:

\[ a_n = 20 \cdot (1/2)^n \]

Now we can fill in the response containers:

• Response container 1 (Coefficient of the sequence formula): 20
• Response container 2 (Exponential factor of the sequence formula): \( (1/2) \)