# Question #2e467

May 21, 2015

Answer: $f \left(x\right) = 3 \cdot {0.2}^{x}$

(1) $f \left(- 1\right) = 15 \implies 15 = a \cdot {b}^{-} 1 \implies 15 = a \cdot \frac{1}{b} \implies a = 15 \cdot b$
(2) $f \left(1\right) = \frac{3}{5} \implies \frac{3}{5} = a \cdot {b}^{1} \implies \frac{3}{5} = a \cdot b$

From (1) we can substitute $a$ with $15 b$ in the equation (2):

$15 \cdot {b}^{2} = \frac{3}{5} \implies {b}^{2} = \frac{3}{75}$ $\implies$ $b = 0.2$ $\implies a = 3$

Our function is $f \left(x\right) = 3 \cdot {0.2}^{x}$