I need some help with my algebra hw

Question

determine a non linear function that is always decreasing and passes through the point

(3/√5, -9/2)

Answer 1

y = b^-x is an always decreasing non linear exponential function

plug in the point

-9/2 = b^(-3/sqr5) solve for b

y= (10^(-sqr5(log-4.5)/3)^-x but that appears undefined

3/sqr5 = about 1.34, -9/2 =-4.5

find a function through (1.34, -4.5)

-4.5= b^1.34

log-4.5 = 1.34logb

logb = (log-4.5)/1.34 = undefined as you can't take the log of a negative number

another approach

take an exponential function

y = e^-x with asymptote y=0

and shift it down so it goes through -4.5

-4.5 = e^-(3/sqr5) + c, solve for c =about -4.76142

y = e^-3/sqr5 - 4.76142 is an always decreasing nonlinear function through (3/sqr5, - 9/2)