Question

evaluate the function to determine the output.
recall: f(2) means to replace the value of n with 2 and perform the operations to find f(n). the point (n, f(n)) is the same location on the graph as (x, y), where n describes the location along the x - axis, and f(n) is the height of the graph.
given that f(n)=2(3^n) and g(n)=5(2^n), evaluate the following functions with the indicated values.

1. f(5)=
2. g(0)=
3. f(2)=
4. g(3)=

Explanation:

Step1: Evaluate $f(5)$

Substitute $n = 5$ into $f(n)=2(3^{n})$. So $f(5)=2\times3^{5}$.
Since $3^{5}=3\times3\times3\times3\times3 = 243$, then $f(5)=2\times243=486$.

Step2: Evaluate $g(0)$

Substitute $n = 0$ into $g(n)=5(2^{n})$. So $g(0)=5\times2^{0}$.
Since any non - zero number to the power of $0$ is $1$, then $g(0)=5\times1 = 5$.

Step3: Evaluate $f(2)$

Substitute $n = 2$ into $f(n)=2(3^{n})$. So $f(2)=2\times3^{2}$.
Since $3^{2}=3\times3 = 9$, then $f(2)=2\times9 = 18$.

Step4: Evaluate $g(3)$

Substitute $n = 3$ into $g(n)=5(2^{n})$. So $g(3)=5\times2^{3}$.
Since $2^{3}=2\times2\times2=8$, then $g(3)=5\times8 = 40$.

Answer:

1. $f(5)=486$
2. $g(0)=5$
3. $f(2)=18$
4. $g(3)=40$