Find the limit of Q(t)?

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In summary: Then, you can solve the differential equation to find the expression for Q(t). In summary, to find the limit of Q(t) as t approaches infinity in this problem, you need to set up and solve a differential equation involving Q(t).
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Homework Statement


A process creates a radioactive substance at the rate of 2 g/hr and the substance decays at a rate proportional to its mass, with constant of proportionality k=0.1(hr)^-1. If Q(t) is the mass of the substance at time t, find the limit of Q(t) as t approaches to infinity.

Homework Equations


None.

The Attempt at a Solution


I know how to take the limit of Q(t) but I need to solve for Q(t) first. And I tried to find it but don't know the formula to solve for Q(t).
 
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  • #2
Math10 said:

Homework Statement


A process creates a radioactive substance at the rate of 2 g/hr and the substance decays at a rate proportional to its mass, with constant of proportionality k=0.1(hr)^-1. If Q(t) is the mass of the substance at time t, find the limit of Q(t) as t approaches to infinity.

Homework Equations


None.

The Attempt at a Solution


I know how to take the limit of Q(t) but I need to solve for Q(t) first. And I tried to find it but don't know the formula to solve for Q(t).

Set up a differential equation for Q(t). Solve it.
 
  • #3
Math10 said:

Homework Statement


A process creates a radioactive substance at the rate of 2 g/hr and the substance decays at a rate proportional to its mass, with constant of proportionality k=0.1(hr)^-1. If Q(t) is the mass of the substance at time t, find the limit of Q(t) as t approaches to infinity.

Homework Equations


None.

The Attempt at a Solution


I know how to take the limit of Q(t) but I need to solve for Q(t) first. And I tried to find it but don't know the formula to solve for Q(t).
You aren't "solving" for Q(t) -- you have to take the given information in the problem and write a differential equation that involves Q(t) based on that information.
 

What is a limit?

A limit is the value that a function approaches as the input variable gets closer and closer to a certain value. In other words, it is the value that the function "approaches" but may not necessarily reach.

Why is finding the limit of a function important?

Finding the limit of a function is important because it helps us understand the behavior of the function, especially near points where the function may not be defined or may be discontinuous. It also allows us to make approximations and predictions about the function's behavior.

What is Q(t)?

Q(t) is a function that depends on a variable t. It could represent any mathematical relationship, such as position, velocity, temperature, or population, that is changing over time.

How do you find the limit of Q(t)?

To find the limit of Q(t), you can use various techniques such as substitution, factoring, and algebraic manipulation. You can also use graphical methods or calculus techniques such as derivatives and integrals.

What are some common types of limits?

Some common types of limits include finite limits, infinite limits, and limits at infinity. Other types include left-hand and right-hand limits, one-sided limits, and limits involving trigonometric, exponential, and logarithmic functions.

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