The intensity of light LLL measured at a depth rrr inside a specific mineral solution is modeled by the function
L(r)=(4+αr)−2,∣αr∣<4 L(r) = (4 + \alpha r)^{-2}, \quad |\alpha r| < 4 L(r)=(4+αr)−2,∣αr∣<4where α\alphaα is a non-zero attenuation constant. The series expansion for this model is given by
L(r)=A+Br+Cr2+Dr3+… L(r) = A + Br + Cr^2 + Dr^3 + \dots L(r)=A+Br+Cr2+Dr3+…where A,B,CA, B, CA,B,C and DDD are constants.
Find the value of AAA.
Given that C=−9BC = -9BC=−9B
show that α2−24α=0\alpha^2 - 24\alpha = 0α2−24α=0.
Hence (i) find the value of α\alphaα (ii) find the value of DDD.
