Let s(t) be the distance of a truck to an intersection (the truck is traveling a

Question

Let s(t) be the distance of a truck to an intersection (the truck is traveling away from the intersection). At time t = 0, the truck is 50 meters from the intersection, is traveling at a velocity of 24 m/s, and begins to slow down with an acceleration of a = -3 m/s2. Determine the second Maclaurin polynomial of s(t), and use it to estimate the truck's distance from the intersection after 2 s. m A bank owns a portfolio of bonds whose value P(r) depends on the interest rate r (measured in percent; for example, r = 5 means a 5% interest rate). The bank's quantitative analyst determines that P(5) = 100,000 dP/dR|r = 5 = -40,000 d2P/d2r|r = 5 = 50,000 In finance, this second derivative is called bond convexity. Find the second Taylor polynomial of P(r) centered at r = 5 and use it to estimate the value of the portfolio if the interest rate moves to r = 5.5%. $ =

Explanation / Answer

Trucks distance is 80 + 24t - 3/2 t^2

at 2 secs

distance = 80 + 24 * 2 - 1.5 * 4 = 80 + 48 -6 = 122meters

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