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The functions f(x) and g(x) are described using the following equation and table: f(x)=4(1.02)^x

Graph in picture

Which statement best compares the y-intercepts of f(x) and g(x)?

AThe y-intercept of f(x) is equal to the y-intercept of g(x).
BThe y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
CThe y-intercept of g(x) is equal to 2 times the y intercept of g(x)
DThe y intercept of g(x) is equal to 2 plus the y intercept of f(x).

The functions f(x) and g(x) are described using the following equation and table: f(x)=4(1.02) x Graph in picture Which statement best compares the y-intercepts class=

Verified Answer :

Answer:

Option: D is the correct answer.

     D.  The y intercept of g(x) is equal to 2 plus the y intercept of f(x).

Step-by-step explanation:

We know that the y-intercept of a function is the y-value of the point where the x-value is zero.

i.e. it is the value of the function  where x=0.

The function f(x) is given by:

\(f(x)=4\times (1.02)^x\)

Now, when x=0 we have:

\(f(0)=4\times (1.02)^0\\\\i.e.\\\\f(0)=4\)

and after looking at the table of values of the function f(x) we observe that:

when x=0      g(x)=6.

This means that the y-intercept of function f(x) is : 4

and the y-intercept of the function g(x) is : 6

i.e. y-intercept of the function g(x) =2+y-intercept of function f(x)

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