regression equation : y = 3.915(1.106)^x. which two equations below could you solve to find d, the number of…

Explanation:

Step1: Understand the problem

The initial population is given by the regression - equation $y = 3.915(1.106)^x$. When the population doubles, if the initial population is $y_0=3.915(1.106)^0 = 3.915$, the new population $y = 2y_0$.

Step2: Set up the equation

Since $y_0 = 3.915$, when the population doubles, $y=2\times3.915 = 7.830$. Substituting into the regression equation $y = 3.915(1.106)^x$, we get $7.830 = 3.915(1.106)^D$. Also, if we divide both sides of the equation $y = 3.915(1.106)^x$ by 3.915 first, when $y$ doubles (i.e., $\frac{y}{3.915}$ doubles), we have $2=(1.106)^D$.

Answer:

$2 = 3.915(1.106)^D$ (False), $7.830 = 3.915(1.106)^D$ (True), $7.830 = 3.915(2)^D$ (False), $2 = 1.106^D$ (True) So the correct equations are: $7.830 = 3.915(1.106)^D$ $2 = 1.106^D$