Question

What would the exponential equation be ?

Answer 1

The equation of the exponential function will be:

`f\:\left(x\right)\:=\:ab^x`

`=\:(3)/(2)\left(2\right)^x`

Explanation:

Given the table

Day Bacteria

1 3

2 6

3 12

4 24

5 48

as

• the x values have the same increment i.e. +1

and

• the y values have common ratio i.e. 6/3 = 2, 12/6=2, 24/12=2

so it is indeed an exponential function

As we know that the exponential function is of the form

`f\:\left(x\right)\:=\:ab^x`

As we know that the y-intercept of
`f\:\left(x\right)\:=\:ab^x` is (0, a).

so

`(3)/(a)=2` ∵ common ratio = successor y-value ÷ previos y-value

`a=(3)/(2)`

so the value of a will be: 3/2

We also know that the common factor i.e. multiplier is 2 in this table, we know the value for b is 2.

Therefore, the equation of the exponential function will be:

`f\:\left(x\right)\:=\:ab^x`

`=\:(3)/(2)\left(2\right)^x`