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

quadratic
quadratic

linear
linear

exponential decay
exponential decay

exponential growth
exponential growth

Answer 1

To determine the type of function represented by the data in the table, let's examine the values of \( y \) in relation to \( x \):

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

Observing the pattern:

- From \( 0.08 \) to \( 0.4 \) (increase by 5 times)
- From \( 0.4 \) to \( 2 \) (increase by 5 times)
- From \( 2 \) to \( 10 \) (increase by 5 times)

The growth in the number of bacteria indicates that \( y \) is increasing by a multiplicative factor rather than just additive, which suggests exponential growth.

Based on this analysis, the type of function represented by the data is **exponential growth**.