# How do you find the exponential function f(x) = Ca^x whose points given are (-1,3) and (1,-4/3)?

Feb 22, 2016

Write a systems of equations to represent the problem.

#### Explanation:

C and a will be our variables.

$3 = C \times {a}^{-} 1$

$- \frac{4}{3} = C \times {a}^{1}$

$- \frac{4}{3 a} = C$

$3 = - \frac{4}{3 a} \times \frac{1}{a}$

$3 = - \frac{4}{3 {a}^{2}}$

$3 \left(3 {a}^{2}\right) = - 4$

$9 {a}^{2} = - 4$

${a}^{2} = - \frac{4}{9}$

$a = \sqrt{- \frac{4}{9}}$

There is no real solution, so your points must be incorrect, as Gió remarked.
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