Find a formula for an exponential function satisfying f16and

Find a formula for an exponential function satisfying f(1)=6|and f(3)=d| your answer will be the items of the parameter of f(x)=|

Solution

let the exponential function be f(x) = a b^x

given f(1) = 6

==> 6 = a b¹

==> 6 = a b

==> a = 6/b

==> f(x) = (6/b) b^x

==> f(x) = 6 b^{x -1}

f(3) = d

==> d = 6 b^3-1

==> d = 6 b²

==> b² = d/6

==> b = (d/6)

==> f(x) = 6 ( (d/6) )^x

Hence f(x) = 6 (d/6)^x/2