Mathias is growing a mold culture in a petri dish. After gathering data for several weeks, he determines the expression for the amount of mold spores in his culture on a certain day. The expression is shown.

Question

2330 left-parenthesis 1.03 right-parenthesis Superscript t Baseline

Question
What does 1.03 in the expression represent?

Answer options with 5 options
A.
It is the starting amount of mold in the culture.

B.
It shows that the growth rate of the culture is 3%.

C.
It shows that the growth rate of the culture is 103%.

D.
It shows that the growth rate of the culture is 1.03%.

E.
It is the amount of mold in the culture at the end of the experiment.

Answer 1

The expression for the amount of mold spores in the culture is given by:

\[ 2330 (1.03)^t \]

In this expression, the term \( 1.03 \) represents the growth factor of the culture. Specifically, it indicates how the amount of mold spores increases with each time unit (where \( t \) is the time in weeks, days, or whatever unit is appropriate).

To interpret this, we observe that:

• A growth factor of \( 1.03 \) means that for every unit of time (e.g., day or week), the amount of mold spores increases by 3%. This is because \( 1.03 \) can be broken down as \( 1 + 0.03 \), where \( 0.03 \) represents the 3% growth.

Based on this reasoning, the correct answer is:

B. It shows that the growth rate of the culture is 3%.