Question

3. **Bacteria in a culture are growing exponentially with time, as shown in the table below. Write an equation that expresses the number of bacteria, y, present at any time t.

Answer 1

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,

`y=a\cdot b^x`

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,

`\begin{gathered} b=\frac{\text{second value}}{first\text{ value}} \\ b=(400)/(200) \\ b=2 \end{gathered}`

x represents the time t.

Now, substitute the obtained values in the general equation.

`y=200\cdot(2)^t`

Hence, the required exponential function is, y = 200(2)^t.