Answer :
The exponential function is, y = 200(2)^t.
Given:
The exponentially growing bacteria is shown intable.
The objective is to write exponential equation for the table values.
The general equation of exponential grwoth is,
[tex]y=a\cdot b^x[/tex]Here,
a represents the inital population of bacteria.
b represents the grow rate.
x represents the time.
From the given table, the value of a is 200.
The value of b can be calculated by find the ratio of second value by first value,
[tex]\begin{gathered} b=\frac{\text{second value}}{first\text{ value}} \\ b=\frac{400}{200} \\ b=2 \end{gathered}[/tex]x represents the time t.
Now, substitute the obtained values in the general equation.
[tex]y=200\cdot(2)^t[/tex]Hence, the required exponential function is, y = 200(2)^t.