Question

Which is an exponential decay function f (x)=3/4 (7/4)x f (x)=2/3 (4/5)-x. F (x)=3/2 (8/7)-x f (x)=1/3 (9/2)x

Answer 1

The given functions are

`1.\, f(x)= (3)/(4)( (7)/(4))^(x) \\ \\2.\,f(x)= (2)/(3)( (4)/(5) ) ^(-x)\\\\3.\, f(x)= (3)/(2) ( (8)/(7) )^(-x)\\\\4.\,f(x)= (1)/(3) ( (9)/(2) )^(x)`

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:
`f(x)= (3)/(2) ( (8)/(7) )^(-x)`