Based on the growth rates of large modern reptiles such as the Galapagos tortoise and examinations of fossils of juvenile dinosaurs, scientists estimate that the largest dinosaurs probably lived to be between 100 and 200 years old.
(A) Based on the growth rates of large modern reptiles such as
Based is the -ED verbal modifier which modifies the noun after comma, which is Scientist. In this way option A, C and E distorts the intended meaning.
(B) On the basis of growth rates of large modern reptiles such as
"On the basis" is a prepositional phrase modifier , which can modify a noun placed away. In this sentence prepositional phrase modifier correctly modifies dinosaurs which is placed slight away in the sentence. Also Such is used to given example , which is the correct usage.
(C) Based on the growth rates of large modern reptiles like
Reason explained in option A
(D) On the basis of growth rates of large modern reptiles, like those of
"On the basis" correctly modifies dinosaur but like is used to give example which is incorrect.
(E) Based on such growth rates as those of large modern reptiles like
Reason explained in option A