determining $a$ and $b$ values in an exponential growth scenario

a population of 240 birds increases at a rate of 16% annually. jemel writes an exponential function of the form $f(x) = ab^x$ to represent the number of birds after $x$ years. which values should she use for $a$ and $b$?

$a =$
$b =$

Question

determining $a$ and $b$ values in an exponential growth scenario

a population of 240 birds increases at a rate of 16% annually. jemel writes an exponential function of the form $f(x) = ab^x$ to represent the number of birds after $x$ years. which values should she use for $a$ and $b$?

$a =$
$b =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions", "Exponential Growth" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Exponential Growth" ] } ## Identify the initial value $a$ $$ a = 240 $$ ## Determine the growth factor $b$ $$ \begin{aligned} r &= 16\% = 0.16 \ b &= 1 + r = 1 + 0.16 = 1.16 \end{aligned} $$ A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form $f(x) = ab^x$ to represent the number of birds after $x$ years. Which values should she use for $a$ and $b$? $a =$ 240 $b =$ 1.16 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Growth" ] }

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Question

Explanation:

Identify the initial value \(a\)

Determine the growth factor \(b\)

Answer: