a colony of 800 ants is decaying by 13% daily. which equation below could be used to find the number of ants for any specific day? let $n$ represent the number of ants left in the colony and let $d$ represent the number of days.

$n = 800(0.87)^d$
$n = 800 + 13^d$
$n = 800(0.13)^d$
$n = 800d + 0.87$

Question

a colony of 800 ants is decaying by 13% daily. which equation below could be used to find the number of ants for any specific day? let \$n\$ represent the number of ants left in the colony and let \$d\$ represent the number of days.

\$n = 800(0.87)^d\$
\$n = 800 + 13^d\$
\$n = 800(0.13)^d\$
\$n = 800d + 0.87\$

$n = 800(0.87)^d$
$n = 800 + 13^d$
$n = 800(0.13)^d$
$n = 800d + 0.87$

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" ], "new_concepts": [ "Exponential Decay Model" ], "current_concepts": [ "Exponential Functions", "Exponential Decay Model" ] } ## Identify the initial value and decay rate $$ \begin{aligned} a &= 800 \ r &= 0.13 \end{aligned} $$ ## Determine the decay factor $$ b = 1 - r = 1 - 0.13 = 0.87 $$ ## Formulate the exponential decay equation $$ N = 800(0.87)^d $$

(A) $N = 800(0.87)^d$

(B) $N = 800 + 13^d$

(C) $N = 800(0.13)^d$

(D) $N = 800d + 0.87$

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

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QUESTION IMAGE

Question

Explanation:

Identify the initial value and decay rate

Determine the decay factor

Formulate the exponential decay equation

Answer: