# Calculus

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The number of people taking the bus at price p dollars per ticket is given by x=5000(5-p)^1/2.

For what value of P is the demand unitary?

• Calculus -

"Unitary demand" occurs where p*x = constant, which also implies that
dp/p = -dx/x,
which is another way of saying
dx/dp = -x/p

dx/dp = -5000*(1/2)/(5-p)^1/2
= -2500/(5-p)^1/2
= -x/p = -5000*(5-p)^1/2*(1/p)

1 = 2*(5-p)/p
p = 10 - 2p
p = \$3.33

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