Question

The population of butterflies in a zoo exhibit is modeled by the following function, where x represents the number of months

B(x)=435(0.76)x

Which statement best describes this relationship?

A.The population of butterflies is increasing at a rate of 24%.

B.The population of butterflies is increasing at a rate of 76%.

C.The population of butterflies is decreasing at a rate of 24%.

D.The population of butterflies is decreasing at a rate of 76%.

Answer 1

Population of of butterflies is represented by B(x)=435(0.76)x , where x is the number of months

Assuming that 435 indicates the initial population of the butterflies, we can see that the population is reducing, since the initial number 435 is being multiplied by a number that is less than 1 (i.e. 0.76)

Also 1 - 0.76 = 0.24

⇒ The population is decreasing by 0.24 or by 24%

Hence the correct answer is option C.The population of butterflies is decreasing at a rate of 24%.