Answer:
[tex]A=4(8)^t[/tex]
Step-by-step explanation:
Since, growth in the population of the bacteria is an exponential process,
Formula to get the population of the bacteria after 't' hours is,
[tex]A=A_0(b)^t[/tex]
From the table given,
After 1 hour, number of bacteria = 32
32 = [tex]A_0(b)^1[/tex] ------- (1)
After 2 hours, number of bacteria = 256
256 = [tex]A_0(b)^{2}[/tex] ------ (2)
Divide equation (2) by equation (1)
[tex]\frac{A_0(b)^2}{A_0(b)}=\frac{256}{32}[/tex]
b = 8
From equation (1)
32 = 8(A₀)
A₀ = 4
Therefore, rule for the table will be,
[tex]A=4(8)^t[/tex]
