How would I write a power function through the two points (1,9/4),(2,9/32)

Question

Im pretty sure I know how to get the power but I don’t know how to write the equation.

Answer 1

The function you want would be y = Ae^kt.

 

(9/4) = Ae^k and (9/32) = Ae^2k are the 2 equations needed to determine the two parameters.

Pass to logarithms on each side of each equation

 

ln (9/4) = ln A + k

ln (9/32) = ln A + 2k

 

Subtract: ln (9/32) - ln (94) = k => k = ln (1/8)

 

Then A = ln (9/4) - ln (1/8) = ln 918)

 

I will leave it to you to look up the logarithms to get the numerical answer.