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

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.