What is value of the growth factor b, in the exponential function f(t)=ab^t , that would satisfy the pair of points (5,83 and 23,113). Rounded to three decimal places.

Question

What is value of the growth factor b, in the exponential function f(t)=ab^t , that would satisfy the pair of points (5,83 and 23,113). Rounded to three decimal places.

Answer 1

f(t) = ab^t. For given points we have: 83 = ab⁵; 113 = ab²³.

(ab²³)/(ab⁵) = 113/83; b¹⁸ = 113/83; b = (113/83)^1/18 = 1.01729; then a = 83/(113/83)^5/18 = 76.18260