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:

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Answer 2

Answer:

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

Use: (a^n)^m=a^{nm}(an)m=anm

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})^xg(x)=(212)x or g(x)=2^{12x}g(x)=212x .

Now, for x=0

g(0)=2^{12\cdot 0}=2^0=1g(0)=212⋅0=20=1

for x=0.25

g(0.25)=2^{12\cdot 0.25}=2^3=8g(0.25)=212⋅0.25=23=8

For x=0.50

g(0.50)=2^{12\cdot 0.50}=2^6=64g(0.50)=212⋅0.50=26=64

For x= 0.75

g(0.75)=2^{12\cdot 0.75}=2^9=512g(0.75)=212⋅0.75=29=512

and for x=1

g(1)=2^{12\cdot 1}=2^1=4096g(1)=212⋅1=21=4096

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