The amount of ozone, q, in the atmosphere is decreasing at a rate proportional to the amount of ozone present. if time t is measured in years, the constant of proportionality is -0.0025. write a differential equation for q as a function of t.

give the general solution for the differential equation. let c represent the arbitrary constant from integration.
q=c

if this rate continues, approximately what percent of the ozone in the atmosphere now will decay in the next 27 years? round your answer to one decimal.

Differential equation:

Solution of diff equation:

6.3% of the ozone in the atmosphere now will decay in the next 27 years.

Step-by-step explanation:

The amount of ozone in the atmosphere may be found by the following differential equation:

In which r is the constant of proportionality and Q is the amount of ozone. A positive value of r means that the amount of ozone in the atmosphere is going to increase, while a negative value means it is going to decrease.

Solving the differential equation:

We integrate both sides of the differential equation and apply the exponential function. So:

Integrating both sides

Applying the exponential:

In which K is the initial amount of ozone.

So

If this rate continues, approximately what percent of the ozone in the atmosphere now will decay in the next 27 years?

This K-Q(27).

K - 0.9347K = 0.0653.

6.3% of the ozone in the atmosphere now will decay in the next 27 years.

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step-by-step explanation:

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