The general exponential regression equation is
[tex]y=ae^{bx}[/tex]
We get (0,847) and (1, 972) points from the table.
Substitute x=0 and y=847, we get
[tex]847=ae^{b(0)}[/tex]
[tex]847=a[/tex]
Substitute a=847 in the general equation, we get
[tex]y=847e^{bx}[/tex]
Substitute x=1 and y=972, we get
[tex]972=847e^{b(1)}[/tex][tex]e^b=\frac{972}{847}=1.148[/tex][tex]\text{ Substitute a=847 and }e^b=1.148\text{ in general equation, we get}[/tex][tex]y=847(1.148)^x[/tex]
Hence the exponential regression equation is
[tex]y=847(1.15)^x[/tex]
Substitute x=8 to find the number of bacteria after 8 hours.
[tex]y=847(1.15)^8[/tex][tex]y=2590.99[/tex]
Round off,
[tex]y=2591[/tex]
The number of bacteria after 8 hours is 2591 bacterias.
