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expeople1 [14]
3 years ago
8

What is the decay factor of the exponential function represented by the table?

Mathematics
1 answer:
bulgar [2K]3 years ago
8 0

Given:

The table of values of an exponential function.

To find:

The decay factor of the exponential function.

Solution:

The general form of an exponential function is:

y=ab^x              ...(i)

Where, a is the initial value and 0 is the decay factor and b>1 is the growth factor.

The exponential function passes through the point (0,6). Substituting x=0,y=6 in (i), we get

6=ab^0

6=a(1)

6=a

The exponential function passes through the point (1,2). Substituting x=1,y=2,a=6 in (i), we get

2=6(b)^1

2=6b

\dfrac{2}{6}=b

\dfrac{1}{3}=b

Here, b=\dfrac{1}{3} lies between 0 and 1. Therefore, the decay factor of the given exponential function is \dfrac{1}{3}.

Hence, the correct option is A.

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