Question

Find the equation of the exponential function represented by the table below:
х
Y
0
3
1
1.5
2
0.75
3
0.375

Answer 1

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