Question

A scientist is studying the population growth rates of two different types of bacteria under the same laboratory conditions. The number of bacterial cells of type A is represented by the equation shown, where P represents the number of bacterial cells at the end of x hours.
p=2^x+19
The number of bacterial cells of type B is represented by the equation shown, where Q represents the number of bacterial cells at the end of x hours.
Q=3^x+19
Which statement is true?

A. At the end of 21 hours, there will be the same number of bacterial cells of type A and type B.
B. At the end of 18 hours, there will be the same number of bacterial cells of type A and type B.
C. At the end of 1 hour, there will be the same number of bacterial cells of type A and type B.
D. At the end of 3 hours, there will be the same number of bacterial cells of type A and type B.

Answer 1

Answer:

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Answer 2

Concept:

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given:

A scientist is studying the population growth rates of two different types of bacteria under the same laboratory conditions. The number of bacterial cells of type A is represented by the equation shown, where P represents the number of bacterial cells at the end of x hours.

p=2^x+19

The number of bacterial cells of type B is represented by the equation shown, where Q represents the number of bacterial cells at the end of x hours.

Q=3^x+19

Find:

Which statement is true?

A. At the end of 21 hours, there will be the same number of bacterial cells of type A and type B.

B. At the end of 18 hours, there will be the same number of bacterial cells of type A and type B.

C. At the end of 1 hour, there will be the same number of bacterial cells of type A and type B.

D. At the end of 3 hours, there will be the same number of bacterial cells of type A and type B

Solution:

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

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

i.e., x = 1

i.e., P(1) = 2¹ + 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) = 3¹ + 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.

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