Write the differential equation model that fits the given description. (a) the rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. initially, the snowball has a volume of 900 cm3 . (b) for an insect moving along some path, the velocity at time t is proportional to the square root of its position.

a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3

and V(0) = 900

where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to . Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.

(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.

Here again appears a constant B for the "proportional" part. And i wrote the velocity as "the rate of change of the position with respect to te time".

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.