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

the pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation.

the pond will be full by the end of day .

Question

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

the pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation.

the pond will be full by the end of day  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Exponential Equations Algebraically", "Solving Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically", "Solving Exponential Equations", "Exponential Growth Calculation" ] } ## Set up the exponential equation Using the *Solving Exponential Equations* knowledge point $$ 3.915(1.106)^x = 400 $$ ## Isolate the exponential term Using the *Solving Exponential Equations Algebraically* knowledge point $$ (1.106)^x = \frac{400}{3.915} \approx 102.1711 $$ ## Solve for x using logarithms Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} x &= \frac{\ln(102.1711)}{\ln(1.106)}\ x &\approx \frac{4.6266}{0.10075}\ x &\approx 45.9 \end{aligned} $$ ## Determine the day the pond is full Since $x \approx 45.9$, the pond reaches its capacity of 400 water lilies during the 46th day. Therefore, the pond will be full by the end of day 46. The pond will be full by the end of day 46. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Exponential Equations Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the exponential equation

Isolate the exponential term

Solve for x using logarithms

Determine the day the pond is full

Answer: