Question

If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?

dPdt=200
Answer A: d cap p over d t is equal to 200
A

dPdt=200t
Answer B: d cap p over d t is equal to 200 t
B

dPdt=100t2
Answer C: d cap p over d t is equal to 100 t squared
C

dPdt=200P
Answer D: d cap p over d t is equal to 200 cap p
D

dPdt=100P2

Answer 1

Answer:

A. dP/dt = 200

Answer 2

The degree of the variable must be one for linear growth. Then the correct option is B.

What is differentiation?

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

If P(t) is the size of a population at time t.

The differential equations have a linear growth in the size of the population. That means the degree of the variable must be one. And the equation of the population will be quadratic. That is given as

$\rm \dfrac{dP}{dt} = 200t$

In this equation, the degree of the time (t) is one.

Thus, the correct option is B.

More about the differentiation link is given below.

https://brainly.com/question/24062595