The closing price (in dollars) per share of stock of tempco electronics on the tth day it was traded is approximated by p(t) = 20 + 12 sin πt 30 − 6 sin πt 15 + 4 sin πt 10 − 3 sin 2πt 15 (0 ≤ t ≤ 24) where t = 0 corresponds to the time the stock was first listed on a major stock exchange. what was the rate of change of the stock's price at the close of the 15th day of trading?

solution:

The closing price (in dollars) per share of stock of Tempco Electronics on the tth day it was  

traded is approximated by  

P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15 (0 ≤ t ≤ 24)  

where t = 0 corresponds to the time the stock was first listed on a major stock exchange.  

What was the rate of change of the stock's price at the close of the 15th day of trading?  

P'(t) = 12(cos πt/30) - 6 (cos πt/15) + 4(cos πt/10) - 3(cos 2πt/15)  

t = 15  

P'(t) = 12(cos 15π/30) - 6 (cos 15π/15) + 4(cos 15π/10) - 3(cos 30π/15)  

P'(t) = 12(cos π/2) - 6 (cos π) + 4(cos 3π/2) - 3(cos 2π)  

P'(t) = 12(0) - 6(-1) + 4(0) - 3(1) = 6 - 3  

P'(t) = $3 per day RATE OF CHANGE  

the closing price on that day

P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15  

t = 15  

P(t) = 20 + 12 sin 15π/30 − 6 sin 15π/15 + 4 sin 15π/10 − 3 sin 30πt/15  

P(t) = 20 + 12 sin π/2 − 6 sin π + 4 sin 3π/2 − 3 sin 2π  

P(t) = 20 + 12(1) − 6(0) + 4(-1) − 3(0) = 20 + 12 - 0 - 4 - 0 = 20 + 12 - 4  

P(t) = $28 per share close price

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