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 .

Explanation:

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

$$
LATEXBLOCK0
$$

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.

Answer:

The pond will be full by the end of day <blank>46</blank>.