Question

Question Miriam is studying the growth rate of bacteria. She puts the data in the following table, where x represents minutes and y represents the number of bacteria.
x 0 1 2 3
y 0.08 0.4 2 10 Which type of function is represented by the data in the table? (1 point)

Answer 1

To determine the type of function represented by the data in the table, we can analyze the relationship between the values of \( x \) (minutes) and \( y \) (number of bacteria):

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 0.08 \\
1 & 0.4 \\
2 & 2 \\
3 & 10 \\
\hline
\end{array}
\]

1. **Exponential Growth**: The number of bacteria seems to increase rapidly as time goes on, which is characteristic of exponential growth.

To confirm if it behaves exponentially, we can observe the ratios of successive \( y \) values:
- From \( 0.08 \) (at \( x = 0 \)) to \( 0.4 \) (at \( x = 1 \)): \( \frac{0.4}{0.08} = 5 \)
- From \( 0.4 \) (at \( x = 1 \)) to \( 2 \) (at \( x = 2 \)): \( \frac{2}{0.4} = 5 \)
- From \( 2 \) (at \( x = 2 \)) to \( 10 \) (at \( x = 3 \)): \( \frac{10}{2} = 5 \)

Since the ratios are consistent, this suggests that the bacteria count is growing exponentially.

2. **Conclusion**: The function best represented by the data is an **exponential function**. Thus, the type of function represented by the data in the table is an **exponential function**.