A scientist is studying a population of bacteria. She uses the function f(x) = 785(0.38)x to represent the number of bacteria over time.

Question

Which statement is the best interpretation of this function?
Responses
A The initial number of bacteria decreases at a rate of 38% each day.The initial number of bacteria decreases at a rate of 38% each day.
B The initial number of bacteria increases at a rate of 62% each day.The initial number of bacteria increases at a rate of 62% each day.
C The initial number of bacteria increases at a rate of 38% each day.The initial number of bacteria increases at a rate of 38% each day.
D The initial number of bacteria decreases at a rate of 62% each day.

Answer 1

The function \( f(x) = 785(0.38)^x \) represents an exponential decay model, where \( 785 \) is the initial amount of bacteria and \( 0.38 \) indicates the decay factor.

In this function:

• The base \( 0.38 \) indicates that the number of bacteria decreases to \( 38% \) of its previous amount each day. This means that there is a \( 62% \) decrease (since \( 100% - 38% = 62% \)).

So, the best interpretation of this function is:

D The initial number of bacteria decreases at a rate of 62% each day.