If f(x) is an exponential function where f(−3)=3 and f(3.5)=54, then find the value of f(6), to the nearest hundredth.

Answer 1

b^-3 = 3

1/b^3 = 3

b^3 = (1/3)^1/3

b^3.5 = 54

b = (54)^1/3.5

the base of an exponential function cannot be the same for f(-3) and f(3.5), so the

exponential function may need a constant term

f(x) = b^x won't work, try b^x + a

b^-3 + a = 3

b^3.5 + a = 54

subtract

b^3.5 - b^-3 = 51

multiply by b^3

b^6.5 -51b^3 -1 =0

solve for b, then for a, then for f(6)