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

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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

Calculus1
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what do you get for dA/dr ?
Use a order of operation. PEMDAS First to do is the paratheis
you need to find the derivative of A

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How do I find a derivative of something with no variable?
the variable is r
(1.003)^96=96.288 96.288*2700=259977.6
yes the variable is r, and r is 4
that's not the way to do this you need to find a rate of change so you differentiate
You are working out A not dA/dr
how would I work our dA/dr?
dA / dr = 2700* 96(1 + r/1200)^95 * 1/1200
- use the chain rule
so plug in r = 4 and you have your answer
You'll need a calculator for that , of course
259200?
No
It comes to one of the choices
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
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
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.

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