The given functions are
[tex]1.\, f(x)= \frac{3}{4}( \frac{7}{4})^{x} \\ \\2.\,f(x)= \frac{2}{3}( \frac{4}{5} ) ^{-x}\\\\3.\, f(x)= \frac{3}{2} ( \frac{8}{7} )^{-x}\\\\4.\,f(x)= \frac{1}{3} ( \frac{9}{2} )^{x}[/tex]
Evaluate the functions.
1. Because 7/4 > 1 and the exponent is positive,
the function does not decay.
2.Because 4/5 < 1 and the exponent is negative,
the function does not decay.
3. Because 8/7 > 1 and the exponent is negative,
the function decays.
4. Because 9/2 > 1 and the exponent is positive,
the function does not decay.
A composite plot the functions verifies the answer.
Answer: [tex]f(x)= \frac{3}{2} ( \frac{8}{7} )^{-x} [/tex]
