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e-lub [12.9K]
3 years ago
7

Find the equation of the exponential function represented by the table below:

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0

Given:

The table of values.

To find:

The equation of the exponential function represented by the table.

Solution:

The general form of an exponential function is

y=ab^x          ...(i)

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

From the given table it is clear that the function passes through (0,3) and (1,1.5). So, the must be satisfy by these points.

Putting x=0 and y=3 in (i), we get

3=ab^0

3=a(1)

3=a

Putting a=3, x=1 and y=1.5 in (i), we get

1.5=3b^1

\dfrac{1.5}{3}=b

\dfrac{1}{2}=b

Putting a=3 and b=\dfrac{1}{2} in (i), we get

y=3\left(\dfrac{1}{2}\right)^x

Therefore, the required equation for exponential function is y=3\left(\dfrac{1}{2}\right)^x.

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