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=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=(14)x
y equals left parenthesis Start Fraction 1 over 4 End Fraction right parenthesis superscript x baseline

y=10(2)x

Answer 1

To model the growth of cells in a petri dish after x days, we are typically looking for an equation that represents exponential growth. Exponential growth can be expressed in the form:

\[ y = a \cdot b^x \]

where:
- \( a \) is the initial amount of cells,
- \( b \) is the growth factor (which should be greater than 1 for growth),
- \( x \) is the number of time periods (in this case, days).

Looking at the options provided:

1. \( y = 100(0.2)^x \) — This represents a decreasing function (since 0.2 < 1), which is not suitable for modeling growth.

2. \( y = 15(0.99)^x \) — Similar to the first, this also represents a decreasing function (since 0.99 < 1). Therefore, it cannot model growth either.

3. \( y = \left( \frac{1}{4} \right)^x \) — This doesn't have an initial amount separate from the growth factor and is also a decreasing function (since \( \frac{1}{4} < 1 \)).

4. \( y = 10(2)^x \) — This represents an increasing function (since 2 > 1), indicating exponential growth.

Based on the analysis above, the equation that could model the number of cells in the petri dish after x days is:

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