Question

Let the function P represent the population P(d), in thousands of a colony of insects d days after first being measured. A model for P is P(d) = 10 + (1.08)^d.

A) P(d) = 10 + 0.08^d
B) P(d) = 10 - (1.08)^d
C) P(d) = 10 * (1.08)^d
D) P(d) = 10 + 1.08^d

Answer 1

The function representing the population is P(d) = 10 * (1.08)^d. The correct option is C) P(d) = 10 * (1.08)^d.

Step-by-step explanation:

The function given to represent the population of a colony of insects after d days is P(d) = 10 * (1.08)^d. The correct option representing the function is C) P(d) = 10 * (1.08)^d.

To understand this, let's break it down. The function starts with a constant value of 10, representing the initial population. The term (1.08)^d represents the growth factor, where 1.08 is the growth rate and d is the number of days. Multiplying the initial population by the growth factor gives us the population after d days.

For example, if we plug in a value of 5 for d, the population after 5 days would be P(5) = 10 * (1.08)^5.