Question

A declining population of an endangered butterfly is determined to have an exponential rate of decrease of r = -0.02. What is the corresponding value of (symbol) for this population?

a) 0.02
b) 0.98
c) 1.02
d) -0.98
e) -1.02

Answer 1

The exponential rate of decrease r = -0.02 corresponds to a base of the exponential function λ, which is 1 + r, equaling 0.98.

Step-by-step explanation:

The student asks about the corresponding value of (symbol) for a population with an exponential rate of decrease of r = -0.02. This value of r represents a population decrease, as a negative r indicates a declining population. To find the corresponding value, we seek the base of the exponential function, which is usually denoted as λ and can be found by adding 1 to the rate. Thus, the corresponding value of λ is 1 + r, which equates to 0.98 when r is -0.02 (1 - 0.02 = 0.98). Therefore, the correct answer is b) 0.98.