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lubasha [3.4K]
3 years ago
11

Use the table of values to write the exponential function

Mathematics
2 answers:
djyliett [7]3 years ago
7 0

Answer:

\frac{1}{2}(\frac{1}{4}^x)

Step-by-step explanation:

To find the function, compare the y values. Notice that each y value decreases by being divided by 4. This means the base of the exponential is 1/4.

To find the initial value, consider the point (0,0.5). When 1/4 is raised to the 0 power, the value is 1. This leaves that the initial value is 1/2 since 1/2*1 = 0.5.

The function is \frac{1}{2}(\frac{1}{4}^x).

Angelina_Jolie [31]3 years ago
5 0

Answer:

The required function is f(x)=\frac{1}{2}\left(\frac{1}{4}\right)^x.

Step-by-step explanation:

The general exponential function is

f(x)=ab^x           .... (1)

where, a is the initial value and b is growth factor.

From the given table it is clear that the function passes through the points (0,0.5) and (-1,2). It means the equation of function must be satisfied by the points (0,0.5) and (-1,2).

Substitute f(x)=0.5 and x=0 in equation (1), to find the value of a.

0.5=ab^0

0.5=a

The value of a is 0.5.

Substitute a=0.5, f(x)=2 and x=-1 in equation (1), to find the value of b.

2=(0.5)b^(-1)

2=\frac{0.5}{b}

2b=0.5

Divide both sides by 2.

b=\frac{0.5}{2}

b=0.25

The value of b is 0.25.

Substitute a=0.5 and b=0.25 in equation (1).

f(x)=0.5(0.25)^x

f(x)=\frac{1}{2}(\frac{1}{4})^x

Therefore the required function is f(x)=\frac{1}{2}\left(\frac{1}{4}\right)^x.

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