Differential equations

 $y=\frac{5}{\sqrt{x-3}}$   solves a differential equation. What is the domain of y?

•  $x>3$  

•  $x<3$ 

•  $-3<x<3$  

•  $x\ne3$  

 $y=e^{\left(4x+5\right)}-7$  solves a differential equation. What is the range of  $y$  ?

•  $y>-7$  

•  $y<-7$  

•  $y<7$  

•  $y>7$ 

•  $-7<y<7$  

Let $\frac{dy}{dx}=-0.4y$ and  $y=5\$  when  $x=0$  .  

What is the solution for  $y$  ?

•  $y=5e^{-0.4x}$  

•  $y=-0.4e^{5x}$  

•  $y=5e^{-\frac{x}{0.4}}$  

•  $y=0.4e^{\frac{x}{5}}$  

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Let $\frac{dy}{dx}=3\left(y-4\right)\left(y-7\right)$  and 

 $y>0$ .
For what values of  $y$  is  $\frac{dy}{dx}>0$  ?
Mark all that apply.

•  $y>4$ 

•  $y>7$  

•  $0<y<4$  

•  $0<y<7$  

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Tags

CCSS.HSA.REI.A.2

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Write a differential equation for the statement:

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

• $\frac{dP}{dt}=kP$

• $\frac{dP}{dt}=k\left(4-P\right)$

• $\frac{dP}{dt}=kP\left(4-P\right)$

• $\frac{dP}{dt}=\frac{kP}{4-P}$

Which of the following equations solves dy/dt = ky?

• $y=y_0e^{kt}$

• $y=mx+b$

• $y=a\left(x-h\right)^2+k$

• $y=A\sin\left[B\left(x-C\right)\right]+D$

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