Suppose y = C e r x {\textstyle y=Ce^{rx}} is the curve of best fit for ( x 1 , y 1 ) , … , ( x n , y n ) {\textstyle (x_{1},y_{1}),\dots ,(x_{n},y_{n})} . Taking the logarithm, we have that
Since the line of best fit through the points ( x 1 , ln y 1 ) , … , ( x n , ln y n ) {\textstyle (x_{1},\ln y_{1}),\dots ,(x_{n},\ln y_{n})} has slope 3 {\textstyle 3} and passes through ( 0 , − 7 ) {\textstyle (0,-7)} , we know that
Answer: C = e − 7 , r = 3 {\textstyle {\color {blue}C=e^{-7},r=3}} .