Answer:
The equation of the exponential function will be:
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
[tex]=\:\frac{3}{2}\left(2\right)^x[/tex]
Step-by-step 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
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
As we know that the y-intercept of [tex]f\:\left(x\right)\:=\:ab^x[/tex] is (0, a).
so
[tex]\frac{3}{a}=2[/tex] ∵ common ratio = successor y-value ÷ previos y-value
[tex]a=\frac{3}{2}[/tex]
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:
[tex]f\:\left(x\right)\:=\:ab^x[/tex]
[tex]=\:\frac{3}{2}\left(2\right)^x[/tex]
