[BrRsn]

Help with calculus anyone?
We are investigating how the walking speed of ants depends on the pheromone concentration they perceive. Pheromone concentration "c" as a function of distance "r (in cm)" from the centre of the source satisfies "c(r)=1/r". Careful measurements with test ants released at 10cm from the source have shown that the distance of an ant as a function of time t (in seconds) satisfies "r(t) = (10 - t)^(2/3)". Determine the speed of the ant as a function of t, and express the speed of the ant as a function of the pheromone concentration (as an intermediate step, express the speed as a function of the distance "r" itself).


So lost. I get that the derivative of the inverse of r(t)=(10-t)^(2/3) should be my speed, correct? Because the inverse gives me my distance as a Y, and time as my X, and the derivative of that (the slope) would be my rate of speed. Yes/no?

All I know is that I will definitely require implicit differentiation, but a bit lost as to how to do so. I know that concentration = 1/distance .. and that my distance of an ant = (10 - time)^(2/3)


... Should I just solve concentration for distance from the first equation, and make that equal to the second, and use implicit differentiation to differentiate for ... what?

Calc support area sucks full of loud first years talking about getting their N and how no one believes their 6 year old yaris is used.