Question

According to a model, if 100 people see sequence of three letters, 87 of them will recall this sequence immediately after seeing it. The model predicts that this number will decrease by 14% of the number the previous second for each second that passes. Which function represents this model, where fሺtሻ is the predicted number of people who will recall the sequence after t seconds have passed?

Answer 1

The function representing the model where f(t) is the predicted number of people who recall the sequence after t seconds is f(t) = 87e^-0.14t, which is an exponential decay function with an initial value of 87 and a decay rate of 14% per second.

Step-by-step explanation:

The question asks which function represents the model where f(t) is the predicted number of people who will recall a sequence after t seconds have passed, given that initially 100 people recall it and the number decreases by 14% every second. We need to express this situation using an exponential decay model.

The initial number of people who recall the sequence is 87. The function must show a decrease of 14% per second for each subsequent second. This situation is modeled by an exponential decay function, which can be represented as f(t) = Pe-rt where P is the initial amount, r is the decay rate (in this case, 0.14), and t is the time in seconds.

Therefore, the function representing this model is f(t) = 87e-0.14t.