Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

The doomsday is 146 days

Step-by-step explanation:

Given

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

Take integral of both sides

Integrate

To find c; let t= 0

Substitute in

Multiply through by -c

Take exponents of

i.e.

Next:

i.e. 3 months

--- initial number of breeds

So, we have:

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We have the growth term to be:

This implies that:

By comparison:

--- 16 rabbits after 3 months:

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Take -1/100th root of both sides

Recall that:

This implies that:

Make T the subject

Substitute: , and

The doomsday is 146 days

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.