1) In the year 1970, the population of the planet Earth was estimated to be 3.5

Question

1) In the year 1970, the population of the planet Earth was estimated to be 3.5 Billion people and it was growing at a rate of about 2% per year. When does this simple population model, assuming population growth is directly proportional to population size, predict we will reach 10 billion people (by year)?

2) A Turkey comes out of the fridge at a temperature of 35 degrees Fahrenheit. It must be cooked to an internal temperature of 180 degrees in order to be safe to eat. After 1 hour, you check the turkey and it measures 100 degrees. If you put it in an oven set to 200 degrees, using Newton's Law of Heating, how long will it take to cook the Turkey in a pre-heated oven?

3) A 200-Volt electromotive force is applied to an RC series circuit in which the resistance is 1000 ohms, the capacitance 5x10^-6 farad. Find the charge, q(t) on the capacitor if i(0) = .4. Recall that i = dq/dt.

Explanation / Answer

3.Everything you did is just fine.

q(t) = 0.001 + Ce^(-200t)

i(t) = q'(t) = - 200*Ce^(-200t)

Since i(0) = 0.4 ===> - 200*C e^0 = 0.4 ==> C = - 0.002

So the charge q(t) = 0.001 - 0.002e^(-200t).

The current i(t) = - 200*(-0.002) e^(-200t) = 0.4e^(-200t)

Charge and current at t = 0.005 s:

q(0.005) = 0.001 - 0.002e^(-200*0.005) = 0.001 - 0.002e^1 ? - 0.044

i(0.005) = 0.4e^(-200*0.005) = 0.4e ? 1.087

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