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

The question is asking us to find the inverse of the function: f(x) = 2 x^2. The original function is: y = 2 x^2. First we have to interchange x and y and then to solve the function for y. So the 1st step: x = 2 y^2. Then: y^2 = x / 2 . Finally we have to take the square root of both sides of equation: y = sqrt( x / 2 ). The inverse is: f^(-1) ( x ) = sqrt( x / 2 )