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

Answer 1

The function \( f(x) = 785(0.38)^x \) represents the number of bacteria over time, where \( x \) is the time in days.

In this context:

• The number 785 represents the initial quantity of bacteria at \( x = 0 \).
• The base \( 0.38 \) indicates the rate of decay. Specifically, since it is less than 1, it represents a decrease.

To interpret it correctly:

• The value \( 0.38 \) means that each day, the bacteria population retains 38% of its previous population, which implies a decay of \( (1 - 0.38) = 0.62 \) or a decrease of 62%.

Thus, the best interpretation of this function is:

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