elizabethlibauskas
contestada

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.

Respuesta :

Since, population of species A is represented by : [tex]P=2^{x} +19[/tex]

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

i.e., x = 1

i.e., [tex]P(1)=2^{1} +19[/tex]

i.e., [tex]P(1)=2 +19[/tex]

i.e., [tex]P(1)=21[/tex]


Also, since population of species B is represented by : [tex]P=3^{x} +18[/tex]

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

i.e., x = 1

i.e., [tex]P(1)=3^{1} +18[/tex]

i.e., [tex]P(1)=3 +18[/tex]

i.e., [tex]P(1)=21[/tex]


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

Hence, option D is correct.

pjwarner2007

Answer:

D, after a single week

Step-by-step 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.

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