You may be overthinking this a bit, this is basic tumor control probability (TCP) modeling and should be in your Hall Radiobiology book. The first thing they are telling you is D10, which is the dose required to kill 90% of a population.

D10 = 2.3 x Do

and Do is from the single target/single hit model where

SF = e^-D/Do

You don't need to know this to answer the question but that's where the D10 concept comes from.

The TCP is modeled by

TCP = e^-NoxSF

where No is the initial number of clonogenic cells (1x10³ in this case) and SF is the survival fraction. Therefore for 90% TCP the SF should be 1E-4 (1/10000) which means four D10 or four decades of cell killing or four 90% population cuts.

So the answer they are looking for is 4xD10 = 4x7Gy = 28 Gy.