Question

1. the population of bears in a national forest is changing according to the function n(t) = 850 (0.96)^t, where t is the time in years and n(t) is the number of bears. which statement correctly explains how the bear population is changing and the type of function shown? a. the population is decreasing by 4% per year and the type of function shown is an exponential decay function. b. the population is increasing by 96% per year and the type of function shown is a linear decay function. c. the population is decreasing by 96% per year and the type of function shown is an exponential growth function. d. the population is increasing by 4% per year and the type of function shown is a linear growth function.

Explanation:

Step1: Identify Function Type

The function is \( N(t) = 850(0.96)^t \), which is in the form of an exponential function \( y = a(b)^t \). Since \( 0 < b = 0.96 < 1 \), it's an exponential decay function.

Step2: Determine Rate of Change

The base \( 0.96 \) means the population is \( 96\% \) of the previous year's population. The decrease rate is \( 1 - 0.96 = 0.04 = 4\% \) per year.

Step3: Evaluate Options

• Option A: Matches decay (4% decrease, exponential decay).
• Option B: Incorrect (increasing? Linear decay? No).
• Option C: Incorrect (decreasing by 96%? Exponential growth? No).
• Option D: Incorrect (increasing? Linear growth? No).

Answer:

A. The population is decreasing by 4% per year and the type of function shown is an exponential decay function.