Multiple-choice questions on Differential equation.

1) Scientists began studying the elk population in Yellowstone Park in 1990 when there were 600 elk.

They determined thattyears after the study began the population size,N(t), was increasing at a rate proportional to 1200N(t).

If the population was 1100 in year 2000, estimate the size of the elk population in year 2010?

1.population size1144

2.population size 1184

3.population size 1124

4.population size 1184

5.population size1164

2) An initial deposit of $Pis made into an account that earns 4% interest compounded continuously.

Money is then withdrawn at a constant rate of $4000 per year.

Set up the differential equation for the amountA=A(t) (in thousands of dollars) in the account aftertyears.

1.dA/dt = 0.04A4

2.dA/dt = 0.04A+4

3.dA/dt = 4A4

4.dA/dt = 4A+4

5.dA/dt =A-4

3) If the account balance becomes zero after 20 years, what was the amount of the initial deposit $P?

(This value ofPis often called thePresent Valueof the regular withdrawals $4000 over a period ofnyears.)

1.$53233

2.$55067

3.$58521

4.$60148

5.$56828

4) Newton's Law of Cooling asserts that the rate of change of temperature of an object is proportional to the difference between its temperature and the ambient temperature.

A hot poker is immersed in water whose temperature is held constant at 80F. After 4 minutes the temperature of the poker has dropped to 128F, while after 6 minutes it has dropped to 112F. What was the tem- perature of the poker initially?

1.initial temp = 193F

2.initial temp = 188F

3.initial temp = 183F

4.initial temp = 178F

5.initial temp = 173F

5) A flea collar for dogs contains an active ingredient that evaporates at a rate proportional to the amount still present. Half of the ingredient evaporates in the first 19 days after the collar is removed from the protective packaging.

If the collar becomes ineffective after 70% of the active ingredient has evaporated, how many days does the collar remain effective?

1.Days effective = 34

2.Days effective = 31

3.Days effective = 30

4.Days effective = 33

5.Days effective = 32