What would an exponential function be?

Question

the two points are (1,7.5) and (3,16.875)

Thanks

Answer 1

The model follows the equation:

y = C*e^(k*t)

 

thus the ratio of two y values in the data is:

y₁/y₂ = e^(k*t₁)/e^(k*r₂)

 

The ratio of two exponentials is the difference of the exponential arguments, so:

y₁/y₂ = e^(k*(t₁ - t₂))

=> 4/9 = e^(k*(-2))

=> -2*k = ln(4/9)

=> k = 0.4055.

 

substitute the value of k into either equation to solve for C.

7.5 = C*e^(0.4055*1)

=> 7.5 = C*1.5

=> C = 5.

 

thus, the exponential function would be:

 

y = 5*e^(0.4055*t).