Question

A psychologist conducting a memory experiment provided participants with a list of three-letter sequences. Immediately after the experiment, the participants remembered 100% of the sequences. The psychologist found that the percentage of sequences the participants remembered decreased by 30% for every 3 -second interval that passed. Which function best models this situation, where P is the percentage of sequences the participants remembered, and t is the time, in seconds, that passed? A) P(t)=100(0.30)

3t
B) P(t)=100(0.30)
t
C) P(t)=100(0.70)
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t
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D) P(t)=100(0.70)
t

Answer 1

C) P(t) = 100(0.70)^(t/3)

Let's break down the function:

The initial percentage of sequences remembered is 100% (P(0) = 100). This is represented by the 100 in the function.

The percentage of sequences remembered decreases by 30% for every 3-second interval that passes. This decrease is represented by (0.70)^(t/3), where (0.70) is the proportion of sequences remembered after each 3-second interval, and t/3 represents the number of 3-second intervals that have passed.

So, as time passes (t increases), the exponent (t/3) in the function increases, leading to a decrease in the percentage of sequences remembered.

Therefore, the correct function that models this situation is:

P(t) = 100(0.70)^(t/3)

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