regression equation : $y = 3.915(1.106)^x$

which two equations below could you solve to find $d$, the number of days it takes the water lily population to double?

$2 = 3.915(1.106)^d$
$7.830 = 3.915(1.106)^d$
$7.830 = 3.915(2)^d$
$2 = 1.106)^d$

Question

regression equation : $y = 3.915(1.106)^x$

which two equations below could you solve to find $d$, the number of days it takes the water lily population to double?

$2 = 3.915(1.106)^d$
  $7.830 = 3.915(1.106)^d$
  $7.830 = 3.915(2)^d$
  $2 = 1.106)^d$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth Calculation", "Solving Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Growth Calculation", "Solving Exponential Equations", "Exponential Regression" ] } ## Identify the initial population value Using the *Exponential Growth Calculation* knowledge point $$ \begin{aligned} &y = a \cdot b^x \ &a = 3.915 \end{aligned} $$ ## Determine the doubled population value Using the *Exponential Growth Calculation* knowledge point $$ \begin{aligned} &y_{\text{double}} = 2 \cdot a \ &y_{\text{double}} = 2 \cdot 3.915 = 7.830 \end{aligned} $$ ## Set up the equation for the doubled population Using the *Solving Exponential Equations* knowledge point $$ 7.830 = 3.915(1.106)^D $$ ## Simplify the equation to find the growth factor relation Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} &\frac{7.830}{3.915} = (1.106)^D \ &2 = 1.106^D \end{aligned} $$

$2 = 3.915(1.106)^D$

$7.830 = 3.915(1.106)^D$

$7.830 = 3.915(2)^D$

$2 = 1.106^D$

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

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QUESTION IMAGE

Question

Explanation:

Identify the initial population value

Determine the doubled population value

Set up the equation for the doubled population

Simplify the equation to find the growth factor relation

Answer: