Question

A scientist is growing cells in a petri dish. Which of the following equations could model the number of cells in the petri dish after x days?(1 point)
Responses

y=(1/4)^x
y equals left parenthesis Start Fraction 1 over 4 End Fraction right parenthesis superscript x baseline

y=100(0.2)^x
y equals 100 left parenthesis 0.2 right parenthesis superscript x baseline

y=15(0.99)^x
y equals 15 left parenthesis 0.99 right parenthesis superscript x baseline

y=10(2)^x

Answer 1

To model the growth of cells in a petri dish, we typically use exponential growth equations. In these equations, the variable \( y \) represents the number of cells, while \( x \) represents time (in days).

The key characteristics of exponential growth are:
- A positive growth rate results in the population increasing over time.
- A negative growth rate (if applicable) would result in a decline.
- The base of the exponential function should be greater than 1 for growth or between 0 and 1 for decay.

Now, let's analyze the provided equations:

1. \( y = (1/4)^x \)
This represents exponential decay, as the base \( 1/4 < 1 \).

2. \( y = 100(0.2)^x \)
This also represents exponential decay, as the base \( 0.2 < 1 \).

3. \( y = 15(0.99)^x \)
This represents a population that is slowly decaying, as \( 0.99 < 1 \). However, it's a very slight decay.

4. \( y = 10(2)^x \)
This represents exponential growth, as \( 2 > 1 \).

Considering the nature of cell growth, the equation that best models the number of cells increasing over time is:

**\( y = 10(2)^x \)**

This equation represents exponential growth, which is appropriate for modeling the growth of cells in a petri dish.