Differential Equations Problem Set

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

• P=.05e^1000t

• P=1000e^5t

• P=1000e^.05t

• p=lne^1000t

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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

y varies jointly with x and the square of z

• y= kxz²

• y= kx√z

• y= kxz

• kx²z

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

y is proportional to the product of z and the square root of x

• y= z(x²)

• y= kz(x²)

• y= kx√z

• y=zkx

Write a differential equation for the statement:

"The rate of change of P is proportional to the product of P and 4 - P."

• dP/dt = kP

• dP/dt = k(4 - P)

• dP/dt = kP(4-P)

• dP/dt = kP/(4-P)

The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially?

• 1

• About 16

• About 40

• About 53

Tags

CCSS.HSF.LE.A.4

Greenium has a half-life of 23 years and decays following the Law of Exponential Change. After how many years will 80% of an original amount have decayed?

• t = 7.4143 years

• t = 10.2646

• t = 53.4043 years

• t = 74.0341 years

Suppose you deposit $1000 in an account that pays 1.5% annual interest and it increases at a rate proportional to the present amount. How much money will you have after 7 years if the interest is compounded continuously?

• $1110.71

• $7,000

• $10,500

• $36,315,502.67

• About 24.5 minutes

• About 16.5 minutes

• About 32.5 minutes

• About 8 minutes

IDENTIFY WHO IS ON THE PHOTO.

• JAMES REID

• DANIEL PADILLA

• ENRIQUE GIL

• JAYAR EBREO