An exponential function, f(x), passes through the points (2,5) and (8,20). Determine the value of f(25) to the nearest integer.

Question

An exponential function, f(x), passes through the points (2,5) and (8,20). Determine the value of f(25) to the nearest integer. Only an algebraic Solution will receive full credit

Answer 1

assume: f(x) = A(b^x); then: f(8) = A(b⁸) = 20;

and: f(2) = A(b²) = 5

dividing the first equation by the second equation gives: b⁶ = 4; or: b = 4^(1/6) = 1.26;

then: A(1.26²) = 5; or: A = 5/(1.26²) = 3.15; then: f(x) = 3.15(1.26^x);

so that: f(25) = 3.15(1.26²⁵) = 1017.6 ---> 1018