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

$\dfrac{20}{10}=\dfrac{a(b)^2}{ab}$

$2=b$

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

$10=a(2)^1$

$\dfrac{10}{2}=a$

$5=a$

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.