Question

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)

Answer 1

(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
\[A= 5/(2^0.8298)= 2.81295\]