Question

From an environmental study of a certain community it is estimated that there will be Q(p)=p^2 + 3p +1200 units of a harmful pollutant in the air when the population is p thousand. The population is currently 30,000 people and is increasing at the rate of 2000 people per year. At what rate is the level of air pollution increasing currently?

Answer 1

can you do derivatives?

Answer 2

you need to find the rate of change of Q with respect to p... differentiate the expression for Q(p) with respect to p.

Answer 3

Yes derivatives. I'm just really confused about the derivatives

Answer 4

when you take the derivative of a term like x^2, you reduce its exponent by 1, and you multiply it by whatever the exponent used to be...

so (d/dx) of x^2 becomes 2x

Answer 5

differentiate Q(p) with respect to p:

Q(p)=p^2 + 3p +1200

(d/dp) Q(p) = 2p + 3 <<<--- can you see why?

Answer 6

I put dQ/dt= 2000(2p + 3)
=4000p + 6000
=4000(30,000) + 6000
=120006000

Answer 7

I think once you have dQ/dp = 2p + 3
then you substitute in p = 30,000... that's the current population.
the rate of change of Q when p = 30,000
will be 2(30000) + 3 = 60,003

the population increase of 2000 is a "trick" to distract you... you just need to worry about the rate of change of the pollution, not the population

Answer 8

I think I made an unpleasant error... I am very sorry!

Answer 9

that expression I just showed was the dQ/dp...

but you were correct when you were thinking that you needed dQ/dt, not dQ/dp

Answer 10

uggh! Apologies again... that was an awful error I made.

Answer 11

thats ok! I appreciate your help! so would the expression and answer be the same?

Answer 12

I am not sure... I was trying to look it up somewhere and learn it (again) really quick.

Answer 13

I'm thinking maybe you might want to copy and paste your question into a new question and close this one... the discussion above is confusing... might be better to start fresh and get someone who knows for sure how to do this.

Answer 14

Ok thank u!