Differential Equations and Rates

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

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

dy/dx = 2x/e^2y find the general solution

• y = ln (2x/2 + C)

  2

• y = ln(2x/2)+c

• y = e^2x+c

• y = mx+b

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

• 𝑦 = ln(15t)

• 𝑦 = 16t³

• 𝑦 = (2𝑡³ − 16)^1/2

• 𝑦 = (2𝑡³ −16)

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.5

Which choice below represents this slope field?

• dy/dx = 2x

• dy/dx = -x

• dy/dx = x

• dy/dx = x²

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

dy/dx = 4x/y.  Suppose y(0)=1
The particular solution is

• B
• C
• D
• E

Tags

CCSS.HSA.REI.A.1

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

Tags

CCSS.HSF.IF.B.4

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

Based on the table, use LRAM and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) 

• 5(3) + 1(4) + 2(5) + 1(7)
• 5(4) + 1(5) + 2(7) + 1(6)
• 5(3) + 6(4) + 8(5) + 9(7)
• 0(3) + 5(4) + 6(5) + 8(7)

Tags

CCSS.HSF.IF.B.4

The population of a town grows at a rate of r(t) people per year (where t is time in years).  What does  $\int_2^4r\left(t\right)dt$  represent?

• The time it took for the town to grow from a population of 2 people to a population of 4 people.

• The number of people in the town on the fourth year.

• The average rate at which the population grew between the second and the fourth year.

• The change in the number of people between the second and the fourth year.

 The temperature in a room changes at a rate of  $r\left(t\right)=\ln\left(t+1\right)\sin\left(t\right)$   degrees Celsius per hour (where t is the time in hours).  At t = 1 hour, the temperature is 18 degrees Celsius.
What is the room's temperature at time t = 3 hours?

• 1.571 degrees C

• 19.571 degrees C

• 19.323 degrees C

• 1.323 degrees C