Question

example: recall that f(2) means to replace the value of n with 2 and work the problem to find f(n). the point (n, f(n)) would be the location on a coordinate plane where n describes the location along the x - axis, and f(n) is the height of the graph. given that f(n)=3(2)^n and g(n)=8(5)^n, evaluate the following functions with the indicated values. 9. f(5)= 10. g(0)= 11. f(2)= 12. g(3)=

Explanation:

Step1: Substitute $n = 5$ into $f(n)$

Given $f(n)=3(2)^{n}$, when $n = 5$, we have $f(5)=3\times(2)^{5}$.
Since $(2)^{5}=2\times2\times2\times2\times2 = 32$, then $f(5)=3\times32=96$.

Step2: Substitute $n = 0$ into $g(n)$

Given $g(n)=8(5)^{n}$, when $n = 0$, we use the rule $a^{0}=1$ ($a
eq0$). So $g(0)=8\times(5)^{0}=8\times1 = 8$.

Step3: Substitute $n = 2$ into $f(n)$

Given $f(n)=3(2)^{n}$, when $n = 2$, we have $f(2)=3\times(2)^{2}$. Since $(2)^{2}=4$, then $f(2)=3\times4 = 12$.

Step4: Substitute $n = 3$ into $g(n)$

Given $g(n)=8(5)^{n}$, when $n = 3$, we have $g(3)=8\times(5)^{3}$. Since $(5)^{3}=5\times5\times5 = 125$, then $g(3)=8\times125=1000$.

Answer:

1. $f(5)=96$
2. $g(0)=8$
3. $f(2)=12$
4. $g(3)=1000$