## anonymous 5 years ago Determine the coefficients A and ^ so that the graph of the function y=Ax^α passes through the points (x,y)=(2,5) and (x,y)=(3,7)

(x,y)=(2,5) $5=A(2)^{\alpha}$ (x,y)= (3,7) $7=A(3)^{\alpha}$ take raito of both, we have $5/7= A(2)^\alpha/(A(3)^\alpha)$ $5/7= (2\3)^\alpha$$\ln(5/7)=\ln(2/3)^\alpha= \alpha \ln(2/3) => \alpha= \ln(5/7)/\ln(2/3)$ alpha= 0.8298 $A= 5/(2^0.8298)= 2.81295$