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)
Responses

exponential growth
exponential growth

exponential decay
exponential decay

linear
linear

quadratic
quadratic

Answer 1

To determine the type of function represented by the data in the table, we can analyze the growth of the number of bacteria (y) over time (x).

The data provided is:

- At \( x = 0 \), \( y = 0.08 \)
- At \( x = 1 \), \( y = 0.4 \)
- At \( x = 2 \), \( y = 2 \)
- At \( x = 3 \), \( y = 10 \)

Looking at the values of \( y \):
- From \( 0.08 \) to \( 0.4 \) (a factor increase of 5).
- From \( 0.4 \) to \( 2 \) (a factor increase of 5).
- From \( 2 \) to \( 10 \) (a factor increase of 5).

The increases are not constant (i.e., they're not equal, which would indicate linear growth), but they seem to increase by a factor of 5 each time, which suggests that the relationship may be exponential.

Based on this analysis, the type of function represented by the data in the table is:

**exponential growth**.