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Which of the following functions grows the SLOWEST?A.โ„Ž(๐‘ก)=5๐‘ก+๐‘ก5h(t)=5 t +t 5 B.๐‘(๐‘ก)=๐‘ก4โˆ’3๐‘ก+9b(t)=t 4 โˆ’3t+9C.๐‘(๐‘ก)=๐‘ก2โˆ’5๐‘กc(t)= t 2 โˆ’5tโ€‹ D.๐‘“(๐‘ก)=2๐‘กโˆ’๐‘ก3f(t)=2 t โˆ’t 3 E.๐‘‘(๐‘ก)=(1.1)๐‘กd(t)=(1.1) t SUBMITarrow_backPREVIOUS

Question

Which of the following functions grows the SLOWEST?A.โ„Ž(๐‘ก)=5๐‘ก+๐‘ก5h(t)=5 t +t 5 B.๐‘(๐‘ก)=๐‘ก4โˆ’3๐‘ก+9b(t)=t 4 โˆ’3t+9C.๐‘(๐‘ก)=๐‘ก2โˆ’5๐‘กc(t)= t 2 โˆ’5tโ€‹ D.๐‘“(๐‘ก)=2๐‘กโˆ’๐‘ก3f(t)=2 t โˆ’t 3 E.๐‘‘(๐‘ก)=(1.1)๐‘กd(t)=(1.1) t SUBMITarrow_backPREVIOUS

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Solution

To determine which function grows the slowest, we need to look at the highest power of t in each function. This is because the term with the highest power will dominate the function as t grows larger.

A. โ„Ž(๐‘ก)=5๐‘ก+๐‘ก^5 B. ๐‘(๐‘ก)=๐‘ก^4โˆ’3๐‘ก+9 C. ๐‘(๐‘ก)=๐‘ก^2โˆ’5๐‘ก D. ๐‘“(๐‘ก)=2๐‘กโˆ’๐‘ก^3 E. ๐‘‘(๐‘ก)=(1.1)^๐‘ก

The highest powers for each function are as follows:

A: 5 B: 4 C: 2 D: 3 E: t (since 1.1^t is an exponential function)

So, the function that grows the slowest is C. ๐‘(๐‘ก)=๐‘ก^2โˆ’5๐‘ก, because it has the lowest highest power.

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Which of the following time complexities indicates the slowest growing function?

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