which equation represents an exponential function with an initial value of 500?

$f(x) = 100(5)^x$
$f(x) = 100(x)^5$
$f(x) = 500(2)^x$
$f(x) = 500(x)^2$

Question

which equation represents an exponential function with an initial value of 500?

$f(x) = 100(5)^x$
$f(x) = 100(x)^5$
$f(x) = 500(2)^x$
$f(x) = 500(x)^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions", "Y-Intercept" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Y-Intercept" ] } ## Identify the general form of an exponential function $$ f(x) = a \cdot b^x $$ ## Apply the initial value condition $$ \begin{aligned} f(0) &= a \cdot b^0 = a \ a &= 500 \ f(x) &= 500 \cdot b^x \end{aligned} $$ ## Match with the given options $$ f(x) = 500(2)^x $$

(A) $f(x) = 100(5)^x$

(B) $f(x) = 100(x)^5$

(C) $f(x) = 500(2)^x$

(D) $f(x) = 500(x)^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the general form of an exponential function

Apply the initial value condition

Match with the given options

Answer: