Question

An exponential function may have a coefficient. In these cases, the equation is often written as f(x) = ab^x, where a is the real-number coefficient and b is the base. Find the value of f(-3) given that f(2) = 6 and f(0) = 54.

My answer: a = 54, b = 0.33, f(-3) = 1.99.

Answer 1

checking:
from f(2) = 6
6 = a b^2
from f(0) = 54
54 = a b^0
so a = 54 ----> you had that

back in 6 = 54 b^2
b^2 = 6/54 = 1/9
b = 1/3 ---> you had b = 33, which is close but not quite accurate enough

then f(x) = 54(1/3)^x
f(-3) = 54(1/3)^-3
= 54(3)^3
= 54(27) = 1458 ---> you missed that one