Question

Scientists at a local preserve are studying the population of two insect species. They studied a sample of 200 of each species of insects. The population of species A insects doubles each week. The population of species B insects increases by 1000 insects each week.

Part A: Write a function in terms of x to model the function of each species of insect.

A. fA(x)=200×2^x

B. fB(x)=200+1000x

C. fA(x)=200+2x

D. fB(x)=200×2^x

Part B: Which species of insects will have a population after 8 weeks?

A. Species A

B. Species B

C. Both species will have the same population

D. It cannot be determined from the information given

Part C: How many more insects does the larger group have than the other? Justify your answer.

A. The larger group has 200×2^8−200−1000.more insects.

B. The larger group has 200×2^8−200 more insects.

C. The larger group has 1000×8−200 more insects.

D. The larger group has 200×2^8−200+1000 more insects.

Answer 1

The function for species A insects is fA(x)=200×2^x and the function for species B insects is fB(x)=200+1000x. After 8 weeks, the population of species B insects will have increased. The larger group has 200×2^8−200−1000 more insects.

Step-by-step explanation:

Part A:

A. fA(x)=200×2^x

B. fB(x)=200+1000x

Part B:

The population of species B insects will have a population after 8 weeks.

Part C:

The larger group has 200×2^8−200−1000 more insects.