Question

Find the output values of the exponential function g(x) = 4,096x for x = 0, 0.25, 0.50, 0.75, and 1.

Answer 1

Answer:

Given: the exponential function  $g(x)=4096^x$.

Use: $(a^n)^m=a^{nm}$

To find the output values of the exponential function for the given values of x:

we can write the function g(x) as, $g(x)=(2^{12})^x$ or $g(x)=2^{12x}$.

Now, for x=0

$g(0)=2^{12\cdot 0}=2^0=1$

for x=0.25

$g(0.25)=2^{12\cdot 0.25}=2^3=8$

For x=0.50

$g(0.50)=2^{12\cdot 0.50}=2^6=64$

For x= 0.75

$g(0.75)=2^{12\cdot 0.75}=2^9=512$

and for x=1

$g(1)=2^{12\cdot 1}=2^1=4096$

Therefore, the output values of the exponential function for the values of x are; {1, 8, 64, 512, 4096}

Answer 2

Hello,

g(x)=4096^x

g(0)=1

g(0.25)=(2^12)^1/4=2^(12/4)=2^3=8

g(0.50)=(2^12)^(1/2)=2^6=64

g(0.75)=(2^12)^(3/4)=2^9=512

g(1)=4096^1=4096