A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and
realizes it must be stuck in a room. So far its strategy has been this: Go in a straight line until you either hit a wall or escape under the door. When you hit a wall rotate a random amount and then start forward again. Repeat this process until escaped. The man moves at a rate of 0.5 cm/sec
A) Direct Escape = give the room in figure image the man starting position (circle) what are its odds of escaping directly on his first move?
B) How long on average will it take the Mab to escape the room through the crack under the door?
A) Direct Escape = give the room in figure image the man starting position (circle) what are its odds of escaping directly on his first move?
B) How long on average will it take the Mab to escape the room through the crack under the door?
1 answer:
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Answer:
Step-by-step explanation:
exponential function :
where a = y intercept and b = factor ( what you multiply by )
looking at the table the y intercept is at (0,10) so a = 10
so we now have y = 10 * (b)^x
to find the factor we simply plug in one of the ordered pairs.
note that the ordered pair chosen does not effect the outcome
i chose (2,250)
we have y = 10 * (b)^x
(x,y) = (2,250)
250 = 10 * (b)^2
divide both sides by 10
25 = b^2
take the square root of both sides
5 = b
the final equation would be f(x) = 10 * (b)^x