Question

I am asked to find the change of A with respect to r, when r=4
the problem reads:
A=2700[1+(r/1200)]^96

The available choices are:
A) dA/dr= 297.3
B) dA/dr= 216.72
C) dA/dr= 217.44
D) dA/dr= 296.31

I don't understand how to do this even after substituting 4 for the r

Answer 1

what do you get for dA/dr ?

Answer 2

Use a order of operation. PEMDAS First to do is the paratheis

Answer 3

you need to find the derivative of A

Answer 4

How do I find a derivative of something with no variable?

Answer 5

the variable is r

Answer 6

(1.003)^96=96.288
96.288*2700=259977.6

Answer 7

yes the variable is r, and r is 4

Answer 8

that's not the way to do this
you need to find a rate of change so you differentiate

Answer 9

You are working out A not dA/dr

Answer 10

how would I work our dA/dr?

Answer 11

dA / dr = 2700* 96(1 + r/1200)^95 * 1/1200

Answer 12

- use the chain rule

Answer 13

so plug in r = 4 and you have your answer

Answer 14

You'll need a calculator for that , of course

Answer 15

259200?

Answer 16

No

Answer 17

It comes to one of the choices

Answer 18

If you have a graphical calculator you can just type it in as above otherwise it might be better to work out the parentheses first then the exponential (^95), then multiply by 2700 , by 96 and then divide by 1200

Answer 19

Wow, I have no idea how you figured out how to do it like that, but it works.
I will be thinking about this one all day.
Thanks

Answer 20

the derivative dA/dr gives you the rate of change of area with respect to r.
by plugging in r = 4 you get the rate of change when r = 4.