AP Calculus Homework - January 21, 2023

Given the differential equation dP/dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

• A) P=Ce^5t

  B) P= 5e^418t

• A) P=Ce^5t

  B) P= 418e^5t

• A) P=Ce^t

  B) P= 418e^t

• A) P=Ce^10t

  B) P= 418e^10t

Water flows continuously from a large tank at a rate proportional to the amount of water in the tank, modeled by dy/dt = ky.  There was initially 10,000 ft^3 at t=0.  After 4 hours there were 8000 ft^3 remaining.
What is the value of k in the differential equation (calculator)

• -0.050
• -0.056
• -.169
• -.200

The rate at which acreage is being consumed by a plot of kudzu is proportional to the number of acres already consumed at time t. If there are 2 acres consumed when t = 1 and 3 acres consumed when t = 5 , how many acres will be consumed when t = 8?

• 3.750

• 4.000

• 4.066

• 4.600

A sample of Kk-1234 (an isotope of Kulmakorpium) loses 99% of its radioactive matter in 199 hours. What is the half-life of Kk-1234?

• 4 hours

• 6 hours

• 30 hours

• 100 hours

Major purchases like cars depreciate in value. That is, as time goes on, their value goes down. The change in a car’s price is directly proportional to its current value. Suppose you own a car whose trade-in value is presently $9,000. Six months ago, its trade-in value was $9,500.

Which differential equation expresses the trade-in value starting six-months ago?

Major purchases like cars depreciate in value. That is, as time goes on, their value goes down. The change in a car’s price is directly proportional to its current value. Suppose you own a car whose trade-in value is presently $9,000. Six months ago, its trade-in value was $9,500.

What will be the trade in value 6 months from now?

Major purchases like cars depreciate in value. That is, as time goes on, their value goes down. The change in a car’s price is directly proportional to its current value. Suppose you own a car whose trade-in value is presently $9,000. Six months ago, its trade-in value was $9,500.

You plan to get rid of the car when the trade-in value drops to $6,000. When will this be?

• 36 months from now.

• 40 months from now.

• 45 months from now.

• 51 months from now.

The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided the temperature is constant. At 15° C, the pressure is 101.3 at sea level and 87.1 at height h = 1,000 meters.

What is the pressure at the top of Mt. Denali in Alaska, at an altitude of 6187 meters?

• 39.8

• 41.5

• 43.6

• 45.9

The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided the temperature is constant. At 15° C, the pressure is 101.3 at sea level and 87.1 at height h = 1,000 meters.

People usually pass out when the pressure drops below 57% of sea level. At what height in meters will people pass out?

• 3125

• 3398

• 3516

• 3722