regression equation: $y = 3.915(1.106)^x$\nthe pond can hold 400 water lilies. by what day will the pond be…

Explanation:

Step1: Set up the equation

We know that $y = 400$ and $y=3.915(1.106)^{x}$. So, $400 = 3.915(1.106)^{x}$.

Step2: Isolate the exponential term

First, divide both sides of the equation by $3.915$: $\frac{400}{3.915}=(1.106)^{x}$. So, $102.171137=(1.106)^{x}$.

Step3: Take the natural - logarithm of both sides

$\ln(102.171137)=\ln((1.106)^{x})$. Using the property $\ln(a^{b}) = b\ln(a)$, we get $\ln(102.171137)=x\ln(1.106)$.

Step4: Solve for $x$

$x=\frac{\ln(102.171137)}{\ln(1.106)}$. Since $\ln(102.171137)\approx4.626$ and $\ln(1.106)\approx0.1$, then $x=\frac{4.626}{0.101}\approx45.8$.

Answer:

$46$