Differential equations part deux (fruit flies, concentration

[ucci]

The rate of growth of a population of fruit flies is proportional to the size of the population at any instant. If there were 180 flies intially, and 300 flies on the second day, how many flies were there on the tenth day? What is the rate at which the population is growing?

I'm at a loss about how to even begin to solve this problem. So I guess my question is how can I form a differential equation that will help me begin to solve the word problem?


Next Question:

You accidentally inahle some mildly poisonous fumes. Twenty hours later you still feel a bit woozy, so you got to the doctor. From blood samples, she measures a poison concentration of 0.00372 mg/ml and tells you to come back in 8 hours. On the second visit, she measures a concentration of 0.00219 mg/ml.

Let t be the number of hours that have elapsed since you first visited the doctor and let C be the centration of poison in your blood. From biology, you realize the instataneous rate of change of C with respect to t is directly proportional to C. Write a differential equation that relates these two variables and solve the equation using the information given.

I'm confused about how to set a differential quation that is directly proportional.

(dC/dt)= :?:

 

[galactus]

Re: Differential equations part deux

To form the DE from scratch, we can use \(\displaystyle \frac{dP}{dt}=kP\)

\(\displaystyle \frac{dP}{dt}-kP=0\)

We can see that the integrating factor is \(\displaystyle e^{-kt}\)

That leads to \(\displaystyle P(t)=Ce^{kt}\)

But C=180 and P(2)=300

You can use \(\displaystyle A=Pe^{kt}\)

\(\displaystyle 300=180e^{2k}\)

Solve for k (the constant of proportionality) and then once you have that just plug in t=10 to find the number in 10 days.

Apply the same idea to the second problem.

 

[ucci]

Re: Differential equations part deux

Thank you so much!