Torture test for convert function

D(p) = 7400 2p+3 =7400 (2p+3 ) −1

dD dp =−7400 (2p+3 ) −2 (2)  (Chain  Rule)

=−14800 (2p+ 3) −2

p(t) =5 t 1 2 +7

dp dt = 5 2 t − 1 2

dD dt = dD dp dp dt  (Chain  Rule)

We want to find the rate of change of demand with respect to time when time t=4 .

When t=4  , p(4) =5 (4) 1 2 +7=5( 2)+7= 17  , and D(17)= 7400 2(17)+3 = 7400 37 =200

Also, dp dt | t=4 = 5 2 (4) − 1 2 =1.25  and dD dp | t=4 = dD dp | p=17 =−14800 (37) −2 =−10.81

So, the rate of change of demand with respect to time at time t=4  is given by

dD dt | t=4 = dD dp | t=4 dp dt | t=4

=(−10.81 )(1.25 )=−13.51

Now, the % rate of change of demand when time t=4   will be given by

(100)( dD dt | t=4 ) D(p) | t=4 = 100(−13.51 ) 200 =−6.76