Question

the exponential function f is defined by f(x) = ab^x, where a and b are positive constants. if f(n - 1) = f(n) + (82/100)f(n - 1), where n is a constant, what is the value of b?

Explanation:

Step1: Substitute function into equation

$f(n-1) = ab^{n-1}$, $f(n) = ab^n$. So equation becomes:
$ab^{n-1} = ab^n + \frac{82}{100}ab^{n-1}$

Step2: Divide both sides by $ab^{n-1}$

Since $a,b>0$, $ab^{n-1}
eq0$. Divide:
$1 = b + \frac{82}{100}$

Step3: Solve for $b$

$b = 1 - \frac{82}{100} = \frac{18}{100} = 0.18$

Answer:

$\frac{18}{100}$ or $0.18$