Assume that the approval rating of a prime minister is given...

Assume that the approval rating of a Prime Minister is given by the function A(d,e), where d is defence spending (in billions) and e is education spending (in billions). The output of the approval rating A(d,e) itself is a percentage between 0 and 100. It is desirable to predict how changes to defence and education spending impact upon the PM's approval. With current spending at d0 and e0, the rate that approval (in percentage) changes with respect to defence spending (in billions) is measured by Newspoll to be the partial derivative ∂A/∂d(d0,e0) = 6.5, so an increase in defence spending of 1 billion dollars will translate to an increase in approval of 6.5%.

Transcript

00:01 In this problem, it is given that the function a of de denotes the approval rate of a prime minister where d denotes the defense charges and e denotes the education charges.

00:21 And this approval rate is measured in percentage while the defense and education charges are measured in billions.

00:30 And also d note and e not represent the current spending of the defense and education respectively.

00:41 And also we are given that do a by do d at the point d note e note represents the rate of change of the approval rate with respect to the defense charges.

00:54 And it is given to be 7 .1.

00:58 Similarly, it is given that doe by doe at the point d note e note, which is the rate of change of the approval rate with respect to the education charges is 6 .9.

01:13 Also, we are given that the approval rate at a point d ,e in the neighborhood of the point d note e note, can be appropriate.

01:25 Approximated as a of d -0 e -not plus do a by do -d at the point d -e -e -note times d minus d -0 plus do a by do e -at at the point d -0 -0 times e -m minus e -not.

01:48 Now we are given that d a of d -0 -0, which is the current approval rate is 51.

01:57 Also, the defense spending is decreased by 0 .3 billion and the education spending is increased by 0 .7 billion.

02:11 We are asked to find the approximate change in the approval rating.

02:19 So here, we are given that a of d note, e note is 51.

02:24 Rate of change of the approval rating with respect to the defense charges at this point is 7 .1 and with respect to educational charges is 6 .9.

02:38 Now we can use this equation to estimate the change in the approval rate or the approval rate...

Question

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