What Is the Long-Term Behavior of Radioactive Substance Mass Q(t)?

[Math10]

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).

 

[Ray Vickson]

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.

 

[Mark44]

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.