Quick question on exponential decay problem

In summary, the conversation is about a problem and solution involving a definite integral. The final answer is shown to be (r (constant) x0 (constant) / k (constant)) * (1 - e^-60t), but the person doesn't understand why their answer differs. They suspect it may be an algebra issue and ask for clarification on why 1 is subtracted from the e term. It is then pointed out that they may have forgotten to include the lower bound when computing the definite integral. After realizing this mistake, they thank the person for helping them see the obvious.
  • #1
ozone
122
0
I'm attaching the problem as a png. The top half is the question whereas the second half is the solution. I understand everything about the question until the ultimate answer

the final answer is: (r (constant) x0(constant) / k (constant)) * (1 - e^-60t)
as shown.

However I don't understand why my answer differs. I concluded the problem with
(r (constant) x0(constant) / k (constant)) * (-e^-60t)
This doesn't seem to be a basic algebra issue, and It is beyond my comprehension.

Thank you.
 

Attachments

  • problem&solution.png
    problem&solution.png
    32.5 KB · Views: 517
Physics news on Phys.org
  • #2
Did you have the same integral as they did? If so, just looking at the last step where they calculate the definite integral, you must have made an algebra error. If that's not the problem, can you post your work so we can look for where you made a mistake?

Perhaps you forgot the term with the 0 (the lower bound) when computing your definite integral?
 
  • #3
I guess it could just be algebraic. I didn't quite understand why it was that they were taking 1 minus the e term. Could you explain please?
 
  • #4
What is the value of the exponential when the lower limit of integration is taken (t = 0)?
 
  • #5
oh wow now I see.. Thanks for helping me to see the obvious!
(I ignored the lower bound~)
 

Related to Quick question on exponential decay problem

1. What is exponential decay?

Exponential decay is a mathematical function that describes the decrease in value of a quantity over time. It follows a specific pattern where the value decreases by a constant proportion at each time interval.

2. How do you solve a quick question on exponential decay?

To solve a quick question on exponential decay, you need to have the initial value, the decay rate, and the time interval. You can use the formula y = y0 * (1-r)^t, where y0 is the initial value, r is the decay rate, and t is the time interval. Plug in the values and solve for y, which will give you the value at the specific time interval.

3. What is the difference between exponential decay and exponential growth?

The main difference between exponential decay and exponential growth is the direction of change. In exponential decay, the value of the quantity decreases over time, while in exponential growth, the value increases over time. Additionally, exponential decay has a negative growth rate, while exponential growth has a positive growth rate.

4. What are some real-life examples of exponential decay?

Exponential decay can be observed in various natural and man-made phenomena. Some examples include radioactive decay, population growth, and the depreciation of assets over time. It can also be seen in the decay of food, the decrease in medication concentration in the body, and the decrease in the intensity of light as it travels through space.

5. How does the decay rate affect the rate of decrease in exponential decay?

The decay rate is directly proportional to the rate of decrease in exponential decay. This means that the higher the decay rate, the faster the value of the quantity will decrease. For example, a decay rate of 0.2 will result in a faster decrease than a decay rate of 0.1 over the same time interval.

Similar threads

B What is meant by decay constant?
    • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
Normalisation of eigenvectors convention for exponentiating matrices
    • Calculus and Beyond Homework Help
Replies
20
Views
1K
Sinusoidal sequences with random phases
    • Calculus and Beyond Homework Help
Replies
1
Views
722
Instantaneous rates of change. Exponential growth and Decay
    • Calculus and Beyond Homework Help
Replies
1
Views
7K
Solving Radioactive Decay Equations for Beginners
    • Calculus and Beyond Homework Help
Replies
18
Views
3K
Please review a rate of decay problem for me
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Center of mass of spherical shell inside of cone (Apostol Problem).
    • Calculus and Beyond Homework Help
Replies
3
Views
584
I How Does Beta Decay Relate to the Role of W Bosons in Weak Nuclear Force?
    • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
I Estimating decay yields from fits to these distributions
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
MHB Abby's question at Yahoo Answers involving exponential decay
    • General Math
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top