Question

evaluate the function to determine the output. 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 $f(n)$

$f(5)=3\times(2)^{5}$

Step2: Calculate $2^{5}$

$2^{5}=2\times2\times2\times2\times2 = 32$

Step3: Multiply by 3

$f(5)=3\times32=96$

Step4: Substitute $n = 0$ into $g(n)$

$g(0)=8\times(5)^{0}$

Step5: Calculate $5^{0}$

Since any non - zero number to the power of 0 is 1, $5^{0}=1$

Step6: Multiply by 8

$g(0)=8\times1 = 8$

Step7: Substitute $n = 2$ into $f(n)$

$f(2)=3\times(2)^{2}$

Step8: Calculate $2^{2}$

$2^{2}=2\times2=4$

Step9: Multiply by 3

$f(2)=3\times4 = 12$

Step10: Substitute $n = 3$ into $g(n)$

$g(3)=8\times(5)^{3}$

Step11: Calculate $5^{3}$

$5^{3}=5\times5\times5=125$

Step12: Multiply by 8

$g(3)=8\times125 = 1000$

Answer:

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