Question

what are the missing numbers?

Answer 1

Given:

The table of values of an exponential function.

To find:

The missing values in the exponential function.

Solution:

The general exponential function is defined as:

`y=a(b)^x` ...(i)

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

First point from the given table is (1,10). It means, the equation (i) must be true for (1,10).

`10=a(b)^1` ...(ii)

Second point from the given table is (2,20). It means, the equation (i) must be true for (2,20).

`20=a(b)^2` ...(iii)

Dividing (iii) by (ii), we get

`(20)/(10)=(a(b)^2)/(ab)`

`2=b`

Putting
`b=2` in (ii), we get

`10=a(2)^1`

`(10)/(2)=a`

`5=a`

Putting
`a=5,b=2` in (i), we get

`y=5(2)^x`

The required exponential function for the given table of values is
`y=5(2)^x`. So, the missing values are 2 and x, where 2 is in the base and x is in the power.