What is the constant k in the form of solution y(t) = Aexp(kt)?

Thread starter beanryu
Start date Apr 25, 2006
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In summary, the constant k is a proportionality constant that determines the rate of change of a solution over time. It represents the slope of the graph of the solution and is directly related to the initial value A. It is usually measured in units of inverse time and can be determined by using the initial value and a given set of data.

Apr 25, 2006

beanryu

In 440 days, an unknown radioactive substance decays to 30 percent of its original amount.

(a) What is the constant k in the form of solution y(t) = Aexp(kt)?

k=?

First of all... I don't even know what Aexp(kt) mean

does it A^(kt) or what?!

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Apr 25, 2006

dav2008

Gold Member

It means [tex]y(t)=Ae^{kt}[/tex]

FAQ: What is the constant k in the form of solution y(t) = Aexp(kt)?

What is the constant k?

The constant k is a proportionality constant that determines the rate at which the solution y(t) changes over time. It is also known as the exponential growth or decay rate.

What does the value of k represent?

The value of k represents the slope of the graph of the solution y(t) = Aexp(kt). It is a measure of the steepness of the curve and indicates how quickly the solution is changing at any given point.

How is the constant k related to the initial value A?

The value of k is directly related to the initial value A. It affects the initial value by determining the rate at which the solution grows or decays. A larger value of k results in a steeper curve and a faster change in the solution.

What units is the constant k measured in?

The constant k is usually measured in units of inverse time, such as 1/seconds or 1/years, depending on the context of the problem. This is because it represents the rate of change of the solution over time.

How do we determine the value of k from a given set of data?

The value of k can be determined by using the initial value A and the value of the solution y at a later time t. By plugging these values into the equation y(t) = Aexp(kt) and solving for k, we can find the constant that best fits the data and represents the rate of change of the solution.