a growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. what is the population of the culture 6 days after inoculation?

$y = 1,000(1.15)^6$; 2,313 bacteria
$y = 1,000(1.15)^7$; 2,660 bacteria
$y = 1,000(1.5)^5$; 7,594 bacteria
$y = 1,000(1.5)^6$; 11,391 bacteria

Question

a growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. what is the population of the culture 6 days after inoculation?

$y = 1,000(1.15)^6$; 2,313 bacteria
$y = 1,000(1.15)^7$; 2,660 bacteria
$y = 1,000(1.5)^5$; 7,594 bacteria
$y = 1,000(1.5)^6$; 11,391 bacteria

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" ] } ## Set up the exponential growth model $$ \begin{aligned} a &= 1,000 \ r &= 0.15 \ y &= a(1 + r)^t \ y &= 1,000(1.15)^t \end{aligned} $$ ## Calculate the population after 6 days $$ \begin{aligned} t &= 6 \ y &= 1,000(1.15)^6 \ y &\approx 1,000(2.31306) \ y &\approx 2,313 \end{aligned} $$

(A) $y = 1,000(1.15)^6$; 2,313 bacteria

(B) $y = 1,000(1.15)^7$; 2,660 bacteria

(C) $y = 1,000(1.5)^5$; 7,594 bacteria

(D) $y = 1,000(1.5)^6$; 11,391 bacteria

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

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Question

Explanation:

Set up the exponential growth model

Calculate the population after 6 days

Answer: