One hundred rats are being trained to run through a maze and are rewarded when they run through it correctly. Once a rat successfully runs the maze, it continues to run the maze correctly in all subsequent trials. The number of rats that run the maze incorrectly after t attempts is given approximately by Find the number of trials required such that only % of the rats are running the maze incorrectly. Round to the nearest trial.

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fichoh fichoh · Answer 1 · 2021-07-01T16:48:12+02:00

Answer:

6 trials

Step-by-step explanation:

The number of rats that run the maze incorrectly after t trials ;

N(t) = 100e^-0.14t

Initial number of rats = 100

45% of rats to run the maze incorrectly ; 45% * 100 = 45 rats

N(t) = 45

N(t) = 100e^-0.14t

45 = 100e^-0.14t

45/100 = e^-0.14t

0.45 = e^-0.14t

Take the In of both sides :

In(0.45) = In(e^-0.14t)

- 0.798507 = - 0.14t

Divide both sides by -0.14

- 0.798507 / - 0.14 = - 0.14t / - 0.14

5.7036 = t

To the nearest whole number :

Number of trials, t = 6 trials