21st November 2019

khanacademy
17

What is the initial value of the exponential function?

For an exponential function the y-intercept is the "initial value" not the common ratio. Consider a standard exponential function of the form y(x) = a•rˣ , if you put in x = 0 you get: y(0) = a•rˣ = a•r° = a•1 = a , so the y-intercept is a , which is called the initial value, not r , which is called the common ratio.

Also question is, what do you mean by initial value problem?

In mathematics, the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.

What is the meaning of the Y intercept in a cost function graph?

Purplemath. In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
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