Which of the following functions grows the SLOWEST?A.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −tB.𝑗(𝑡)=14ln⁡(𝑡200)j(t)= 41​ ln(t 200 )C.𝑎(𝑡)=𝑡52a(t)=t 25​ D.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )E.𝑏(𝑡)=𝑡4−3𝑡+9b(t)=t 4 −3t+9

The function that grows the slowest is D. 𝑖(𝑡)=ln⁡(𝑡100).

Here's why:

A. 𝑔(𝑡)=3𝑡2−𝑡 is a quadratic function, which grows faster than a logarithmic or linear function.

B. 𝑗(𝑡)=14ln⁡(𝑡200) is a logarithmic function, which grows slower than a quadratic or polynomial function, but faster than a simple logarithmic function.

C. 𝑎(𝑡)=𝑡52 is a polynomial function of degree 5/2, which grows faster than a quadratic, logarithmic or linear function.

D. 𝑖(𝑡)=ln⁡(𝑡100) is a simple logarithmic function, which grows slower than a quadratic, polynomial or another logarithmic function with a coefficient.

E. 𝑏(𝑡)=𝑡4−3𝑡+9 is a polynomial function of degree 4, which grows faster than a quadratic, logarithmic or linear function.

Logarithmic functions grow slower than polynomial functions, and among the logarithmic functions, the one without a coefficient (D) grows the slowest.