Bacteria are growing in a circular colony one bacterium thick. The bacteria are growing at a constant rate, thus making the area of the colony increase at a constant rate of 12 mm sq. per hour. Find an equation expressing the rate of change of the radius as a function of the radius, r, in millimeters, of the colony. Plot dr/dt as a function of r. How fast is r hanging when it equals 3 mm? Describe the way dr/dt changes with the radius of the circle.

Question

We just started learning related rates problems like the one above but I'm totally stumped on this one.

Answer 1

area=PI8r^2
darea/dt=PI*2 r dr/dt
you are given darea/dt=12mm^2/hr

so dr/dt= 12/(2r) mm/hr

Answer 2

I'm sorry, I'm not following what you did. I get that we know dx/dt = 12mm^2/hr and we want to find dr/dt but I don't know how you linked them together as a function of r. Maybe show me more steps and how you got the derivative dr/dt. Thanks

Answer 3

wow, you are lost.

Start with the relationship
A=PI*r^2
take the derivative with respect to time:

dA/dt=PI*2*r*dr/dt
you are given dA/dt. Solve for dr/dt

Why are you stuck with using x as a variable? The world is more generous than that.

Answer 4

12mm^2/hr = r2PI dr/dt

So 12/2PIr mm^2/hr = dr/dt
which is the same as dr/dt = 6/PIr mm^2/hr

Why'd you originally say dr/dt= 12/(2r) mm/hr

Answer 5

I must have dropped a PI.

Answer 6

now all u got to do is plug in the 3 for r and u will get the answer