physics question help please

hi, please could I have some help with question 5c of this paper? https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FPhysics%2FA-level%2FPast-Papers%2FCAIE%2FPaper-2%2FQP%2FNovember%202021%20(v1)%20QP.pdf

I thought since V=E-Ir the terminal volts will decrease but P=V2/R and resistance is also changing so I wasn't really sure?
Thanks!

In the previous part, the battery has negligible internal resistance, so V = E. The total resistance R_tot = 10 Ω.
Power produced by the battery is E^2/R_tot = V^2/R_tot
In (c), the battery has internal resistance says r, so V = E - Ir, this means there is a reduction in terminal p.d. V but the external total resistance is still 10 Ω.
Power produced by the battery becomes E^2/(10 + r) NOT V^2/10.

Oh, so is power produced by a battery always equal to Emf^2/ total resistance?

Yes
OR
(total current)^2 * (total resistance)
OR
(total current)(EMF)

Just out of curiosity, why do we not use terminal pd?

We use terminal p.d. and total external resistance to find useful power output.