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

quadratic
quadratic

linear

Answer 1

To determine the type of function represented by the data in the table, let's analyze the growth of the bacteria as the minutes (x) increase.

The data provided is as follows:

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

Now let's observe the growth from one minute to the next:

1. From \( x = 0 \) to \( x = 1 \):
- The growth is from \( 0.08 \) to \( 0.4 \) (a factor of 5 increase).

2. From \( x = 1 \) to \( x = 2 \):
- The growth is from \( 0.4 \) to \( 2 \) (a factor of 5 increase).

3. From \( x = 2 \) to \( x = 3 \):
- The growth is from \( 2 \) to \( 10 \) (a factor of 5 increase).

The increases show a consistent pattern of multiplicative growth rather than additive, which suggests that the data represents **exponential growth**.

Therefore, the type of function represented by the data in the table is:

**Exponential growth.**