How Many Licks Tootsie Roll Help

[madeeeeee]

"How Many Licks" Tootsie Roll Help

1. Homework Statement [/b]
In an activity, i was supposed to determine the rate of change of volume of a tootsie rool as i consume it.

My initial radius is 1.21 cm at t=0 sec

the rest of my data is

30 sec- 1.27 cm
60 sec-1.25 cm
90 sec- 1.24 cm
120 sec- 1.22 cm
150 sec- 1.21 cm
180 sec- 1.21 cm
210 sec- 1.20 cm
240 sec- 1.19 cm
270 sec- 1.18 cm
300 sec- 1.16 cm

1. Determine the rate of change of the TRP for you mouth power.

Answer:
dr/dt = 1.25-1.27 / 90-60 = -0.00067 cm/s

did i do this right?

2. If you consumed it consistently what model should you find?
I graphed it and it showed the line decreasing with respect to time.
So does this mean that it is a decreasing exponential function?

3. Determine how fast the volume of the lolly pop is decreasing when the radius is thre fourths of the original value.

My original radius was 1.27 cm and 3/4 of that is 0.9525 cm

i know that the volume of the sphere is 4/3(pi)(r)^3

V=4/3(pi)(.9525)^3
= 3.62 cm
Did i do this right?

Now it asks for dV/dt=

i don't understand what this means, can someone explain the formulas and steps to get my answer. Maybe chain rule

 

[lippyka]

or implicit differentiation?Answer: To determine the rate of change of volume when the radius is 3/4 of the original value, you need to use the chain rule. The chain rule states that if y is a function of x, then the derivative of y with respect to x is equal to the derivative of y with respect to u times the derivative of u with respect to x. In this case, you have the volume V of a sphere (which is a function of the radius r) and you want to determine the derivative of V with respect to time t. Therefore, you can use the chain rule by first finding the derivative of V with respect to r, and then finding the derivative of r with respect to t.The formula for the volume of a sphere is V = 4/3(pi)(r)^3. Therefore, the derivative of V with respect to r is dV/dr = 4/3(pi)(3r^2).Now, you need to find the derivative of r with respect to t. Since you know that the radius is decreasing over time, you can say that dr/dt is a negative value. To find this value, you can use the data points that you were given in the activity. At t = 30 sec, the radius was 1.27 cm. At t = 90 sec, the radius was 1.25 cm. Therefore, the derivative of r with respect to t is dr/dt = 1.25 - 1.27 / 90 - 30 = -0.00067 cm/s. Finally, you can use the chain rule to find the derivative of V with respect to t. Using the values that you calculated above, you can say that dV/dt = (4/3(pi)(3r^2))(-0.00067 cm/s) = -0.0019 cm3/s. This is the rate of change of the volume of the lollipop when the radius is 3/4 of the original value.