Calculate the Rate of Increase for Doubling Radius of an Ink Spot

In summary, the problem involves finding the rate of increase (in cm/s) at the time when the radius of a circular ink spot has doubled from its initial value. The formula for the radius at time t is r=\frac{1+4t}{2+t}. After analyzing the problem and checking the calculations, the rate of increase is 9/7cm/s, not 7/9cm/s as originally thought.
  • #1
Procrastinate
158
0
The radius of a circular ink spot, t seconds after it first appears, is given by:

[tex]r=\frac{1+4t}{2+t}[/tex]

Find the rate of increase (in cm/s) at the time when th radius as doubled from its initial value.



I have attached my working; however, the answer is 7/9cm/s and I keep getting 9/7cm/s. Does that even make sense if it is doubling anyways?
 

Attachments

  • scan0014.jpg
    scan0014.jpg
    27.1 KB · Views: 371
Physics news on Phys.org
  • #2
I don't see any problem with your work; it seems to me that 9/7 is right. 7/9 is the rate of change at t=1, but that doesn't correspond to the condition given in the problem, since the initial radius is 1/2 and the radius at t = 1 is 5/3.
 

FAQ: Calculate the Rate of Increase for Doubling Radius of an Ink Spot

What is the "rate of increase" question?

The "rate of increase" question refers to a common question asked in scientific research, particularly in the field of population growth or change. It asks about the rate at which a particular phenomenon or variable is increasing over time.

How is the "rate of increase" calculated?

The "rate of increase" is typically calculated by dividing the difference between the final value and the initial value of a variable by the time it took for that change to occur. This can be expressed as a percentage or a decimal value.

Why is the "rate of increase" important in scientific research?

The "rate of increase" is important because it allows scientists to better understand the magnitude and speed of a particular change or phenomenon. This information can help inform future research, policies, and interventions.

How can the "rate of increase" be influenced?

The "rate of increase" can be influenced by a variety of factors, including natural processes, human activities, and environmental conditions. For example, human population growth can be influenced by changes in birth and death rates, migration patterns, and economic conditions.

Can the "rate of increase" be used to make predictions?

Yes, the "rate of increase" can be used to make predictions about future changes or trends. However, it is important to note that predictions are based on current data and assumptions, and can be affected by unforeseen events or changes in the variables being studied.

Similar threads

How Fast is the Radius of a Circle Increasing When a Stone is Dropped in Water?
Replies
3
Views
2K
Related Rates Problem: Solving for Volume Increase with Changing Sphere Radius
Replies
5
Views
2K
Differentiation with units- Related Rates problem
Replies
30
Views
3K
Rate at which a bucket gets filled
Replies
4
Views
2K
Use chain rule to find rate of area increase
Replies
15
Views
3K
Related Rates (increasing cone radius question)
Replies
5
Views
6K
Does the gravitational rate of acceleration increase within a planet?
2
Replies
54
Views
3K
Find at what rate the orbit radius will grow
Replies
30
Views
1K
Constant Rate of Change in Area of Circle with Changing Radius?
Replies
6
Views
2K
MHB Am I doing this related rates right?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top