Question

A scientist is studying the population growth rates of two different species of rats in the same laboratory conditions. The population of species A is represented by the equation below, where P represents the population at the end of x weeks.

P=2^x+19

The population of species B is represented by the equation below, where P represents the population at the end of x weeks.

P=3^x+18

Which statement is true?

A. At the end of 18 weeks, species A and species B will have the same population.
B. At the end of 21 weeks, species A and species B will have the same population.
C. At the end of 3 weeks, species A and species B will have the same population.
D. At the end of 1 week, species A and species B will have the same population.

Answer 1

D, after a single week

Explanation:

from the information given population A starts with one more unit initially, but the difference in growth is also one off, population B grows faster and has an initial value of 18.

The numbers then become 18+3 and 19+2, both adding up to 21.

Answer 2

Since, population of species A is represented by :
`P=2^(x) +19`

Let us find the population of species A, at the end of week 1:

i.e., x = 1

i.e.,
`P(1)=2^(1) +19`

i.e.,
`P(1)=2 +19`

i.e.,
`P(1)=21`

Also, since population of species B is represented by :
`P=3^(x) +18`

Let us find the population of species B, at the end of week 1:

i.e., x = 1

i.e.,
`P(1)=3^(1) +18`

i.e.,
`P(1)=3 +18`

i.e.,
`P(1)=21`

Thus, at the end of 1 week, species A and species B will have the same population.

Hence, option D is correct.