writing a function to model exponential growth

a colony contains 1500 bacteria. the population increases at a rate of 115% each hour. if $x$ represents the number of hours elapsed, which function represents the scenario?

$f(x) = 1500(1.15)^x$
$f(x) = 1500(115)^x$
$f(x) = 1500(2.15)^x$
$f(x) = 1500(215)^x$

Question

writing a function to model exponential growth

a colony contains 1500 bacteria. the population increases at a rate of 115% each hour. if $x$ represents the number of hours elapsed, which function represents the scenario?

$f(x) = 1500(1.15)^x$
$f(x) = 1500(115)^x$
$f(x) = 1500(2.15)^x$
$f(x) = 1500(215)^x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth" ], "new_concepts": [], "current_concepts": [ "Exponential Growth", "Exponential Functions" ] } ## Identify the initial value and growth rate $$ \begin{aligned} a &= 1500 \ r &= 115\% = 1.15 \end{aligned} $$ ## Determine the growth factor $$ \begin{aligned} b &= 1 + r \ b &= 1 + 1.15 = 2.15 \end{aligned} $$ ## Formulate the exponential growth function $$ \begin{aligned} f(x) &= a \cdot b^x \ f(x) &= 1500(2.15)^x \end{aligned} $$

$f(x) = 1500(1.15)^x$

$f(x) = 1500(115)^x$

$f(x) = 1500(2.15)^x$

$f(x) = 1500(215)^x$

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

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QUESTION IMAGE

Question

Explanation:

Identify the initial value and growth rate

Determine the growth factor

Formulate the exponential growth function

Answer: