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 46

which solution method did you use?

• logarithms
• graphing \\(y = 3.915(1.106)^x\\) and tracing
• graphing \\(y = 3.915(1.106)^x\\) and \\(y = 400\\), then finding the x-value of the intersection

Explanation:

Set up the equation for the pond capacity

Using the Solving Exponential Equations knowledge point

$$
LATEXBLOCK0
$$

Solve for x algebraically

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK1
$$

Identify the corresponding solution method

The algebraic solution method used to solve the equation \(400 = 3.915(1.106)^x\) by taking the logarithm of both sides is "Logarithms".

Answer:

Question 1

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

Question 2

• (A) Logarithms (Correct answer)
• (B) Graphing \(y = 3.915(1.106)^x\) and tracing
• (C) Graphing \(y = 3.915(1.106)^x\) and \(y = 400\), then finding the x-value of the intersection