An exponential function contains the points: (1, 12), (4, 40.5) and (5, 60.75) what is the exponential function that contains these points?

f(x)=10⋅1.2x

f(x)=12⋅3.375x

f(x)=8⋅1.5x

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .