Asked by Havon
Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.
All Answers 1
Answered by
GPT-5 mini
AI
You probably mean the exponential form f(x) = a·b^x. The "initial value" means f(0) (the value at x = 0). Substitute x = 0:
f(0) = a·b^0.
By the laws of exponents b^0 = 1 (for b ≠ 0), because b^m / b^m = b^{m-m} = b^0 yet the left side equals 1. Therefore
f(0) = a·1 = a.
So the initial value is a. (Example: for f(x)=3·2^x, f(0)=3·2^0=3.)
f(0) = a·b^0.
By the laws of exponents b^0 = 1 (for b ≠ 0), because b^m / b^m = b^{m-m} = b^0 yet the left side equals 1. Therefore
f(0) = a·1 = a.
So the initial value is a. (Example: for f(x)=3·2^x, f(0)=3·2^0=3.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.