Aradioactive material has a decay rate proportional to the amount of radioactive material present at that time, with a proportionality factor of 2 per unit time. write a differential equation of the form pf(p), which models this situation, where p is the amount or radioactive material micrograms as function of time

a). P' = -2P

b). P' = -2(P + 4t)

Step-by-step explanation:

This question is incomplete; here is the complete question in the form of an attachment.

a). A radioactive material has a decay rate P', is proportional to the amount 'P' of radioactive material present at that time.

Relation that represents this phenomenon will be,

P' ∝ -P

P' = -2P [2 is the proportionality factor]

Here negative notation represents the decay of the substance and P' represents the rate of decay.

b). Now additional amount of  radioactive element is added at the rate of 4 micrograms per unit time.

If the radioactive element has been added for the time 't' then amount of radioactive element after time 't' = (P + 4t)

Now we know decay rate is proportional to the amount of radioactive material at that time.

Therefore, P' ∝ -(P + 4t)

P' = -2(P + 4t)

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step-by-step explanation:

8+8+6+6

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1