Question

Does this table represent an exponential function? x 1 2 3 4 y -2 -12 -72 -432

Answer 1

`f(x)=b(a)^x\\\\\text{From the table}\\\\x=1\to y=-2\ and\ x=2\to y=-12.\\\text{Substitute:}\\\\\left\{\begin{array}{ccc}b(a)^1=-2\\b(a)^2=-12\end{array}\right\\\\\left\{\begin{array}{ccc}b(a)=-2\\b(a)(a)=-12\end{array}\right\\\\\text{substitute from the first equation to the second equation}\\\\-2(a)=-12\qquad\text{divide both sides by (-2)}\\\\a=6\\\\\text{Substitute the value of a to the first equation}\\\\b(6)=-2\qquad\text{divide both sides by 6}\\\\b=-(2)/(6)\to b=-(1)/(3)`

`f(x)=-(1)/(3)(6)^x\\\\\text{check other values of x}\\\\for\ x=3\to f(3)=-(1)/(3)(6)^3=-(1)/(3)(216)=-72\qquad CORRECT\\\\for\ x=4\to f(4)=-(1)/(3)(6)^4=-(1)/(3)(1296)=-432\qquad CORRECT\\\\Answer:\ YES.\ It's\ an\ exponential\ function\ f(x)=-(1)/(3)(6)^x`