Which of the following functions grows the SLOWEST?A.โ(๐ก)=5๐ก+๐ก5h(t)=5 t +t 5 B.๐(๐ก)=๐ก4โ3๐ก+9b(t)=t 4 โ3t+9C.๐(๐ก)=๐ก2โ5๐กc(t)= t 2 โ5tโ D.๐(๐ก)=2๐กโ๐ก3f(t)=2 t โt 3 E.๐(๐ก)=(1.1)๐กd(t)=(1.1) t SUBMITarrow_backPREVIOUS
Question
Which of the following functions grows the SLOWEST?A.โ(๐ก)=5๐ก+๐ก5h(t)=5 t +t 5 B.๐(๐ก)=๐ก4โ3๐ก+9b(t)=t 4 โ3t+9C.๐(๐ก)=๐ก2โ5๐กc(t)= t 2 โ5tโ D.๐(๐ก)=2๐กโ๐ก3f(t)=2 t โt 3 E.๐(๐ก)=(1.1)๐กd(t)=(1.1) t SUBMITarrow_backPREVIOUS
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(๐ก)=5๐ก+๐ก^5 B. ๐(๐ก)=๐ก^4โ3๐ก+9 C. ๐(๐ก)=๐ก^2โ5๐ก D. ๐(๐ก)=2๐กโ๐ก^3 E. ๐(๐ก)=(1.1)^๐ก
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(๐ก)=๐ก^2โ5๐ก, because it has the lowest highest power.
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