explain why the initial value of any function of the form $f(x)=a(b^{x})$ is equal to $a$.
explain why the initial value of any function of the form $f(x)=a(b^{x})$ is equal to $a$.
Answer
Explanation:
Step1: Define initial value
The initial value of a function is the value of the function when (x = 0).
Step2: Substitute (x = 0) into function
Substitute (x=0) into (f(x)=a(b^{x})), we get (f(0)=a(b^{0})).
Step3: Evaluate (b^{0})
By the zero - exponent rule, for any non - zero real number (b), (b^{0}=1). So (f(0)=a\times1=a).
Answer:
The initial value of (f(x)=a(b^{x})) is (a) because when (x = 0), (b^{0}=1) and (f(0)=a\times1=a).