What would the exponential function be?

Question

(-1,1.25) and (3, 0.032)

thanks!

Answer 1

Well, in a standard two parameter model, the exponential function is:

y = C*e^(k*t)

 

Thus, the ratio of two y values:

y₁/y₂ = 1.25/0.032 = e^(k*-1)/e^(k*3)

The ratio of two exponentials is the difference of the values in the exponential, thus:

1.25/0.032 = 39.0625 = e^(-4*k).

Take the natural log of both sides:

-4*k = ln(39.0625)

=> k = -0.9163.

 

From this, substitute k into one equation to get C.

1.25 = C*e^(-0.9163*-1) = 2.5*C

=> C = 0.5

 

So the exponential model is:

 

y = 0.5*e^(-0.9163*t).