Question

5. Write an exponential function of the form y=ab* to represent the table below.(1,2),(2,8),(3,32),(4,128)

Answer 1

`y\text{ = }(1)/(2)(4^x)`Step-by-step explanation:
`\text{Exponenetial form: y = ab}^x`

a = initial value

It is value of y when x = 0

b = constant term in the y values

For the x values, there is an increase in 1

2-1 = 3-2= 4-3 = 1

for the y values:

8/2 = 32/8 = 128/32 = 4

for the y values, the previous term is multiplied by 4 to get the next term

This means b = 4

`\begin{gathered} to\text{ get a:} \\ \text{the previous term before 1, it will be 1-1 = 0} \\ \text{the x = 0} \\ \text{the previous term before 2, it will be }(2)/(4) \\ y\text{ = 1/2} \end{gathered}`

Hence, a which is the value of y when x is zero is 1/2

The table will be represented as:

`y\text{ = }(1)/(2)(4^x)`