Unit 4 Lesson 4

A bacteria population is tripling every hour. By what factor does the population change in  $\frac{1}{2}$  hour? Select all that apply.

•  $\sqrt{3}$  

•  $\frac{3}{2}$  

• 
•  $3^{\frac{1}{2}}$  

•  $3^2$  

A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon. Which expression represents the amount of medication, in milligrams, in the patient's body at 7 p.m. on the same day.

• $225\cdot\left(\frac{1}{2}\right)^{1.75}$

• $225\cdot\left(\frac{1}{2}\right)^7$

• $225\cdot\left(\frac{1}{2}\right)^{0.75}$

• $225\cdot\left(\frac{1}{2}\right)^{\frac{4}{7}}$

A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 225 milligrams to a patient at noon. The expression  $225\cdot\left(\frac{1}{2}\right)^{\frac{5}{2}}$  represents the amount of medicine in the body some time after it is administered. What time is that?

• 5:30 p.m. on the same day

• 7 p.m. on the same day

• 8:30 p.m. on the same day

• 10 p.m. on the same day

The number of employees in a company has been growing exponentially by 10% each year. By what factor does the number of employees change each month?

• $\left(1.1\right)^1$

• $\left(1.1\right)^{\frac{1}{12}}$

• $\left(1.1\right)^{30}$

• $\left(1.1\right)^{\frac{1}{365}}$

The number of employees in a company has been growing exponentially by 10% each year. By what factor does the number of employees change every 3 months?

• $\left(1.1\right)^1$

• $\left(1.1\right)^{\frac{1}{12}}$

•  $\left(1.1\right)^{\frac{1}{4}}$ 

•  $\left(1.1\right)^{\frac{3}{6}}$ 

The value of a truck decreases exponentially since its purchase. The two points on the graph shows the truck's initial value and its value a decade afterward. 

1- Express the car's value, in dollars, as a function of time $d,$  in decades, since purchase.

2- By what factor is the value of the car changing each year? Show your reasoning.

Is the statement true or false: $50^{\frac{1}{2}}=25.$  

• true

• false

Is the statement true or false: $\sqrt{30}is\ a\ solution\ to\ y^2=30.$  

• true

• false

Is the statement true or false: $\sqrt{20}\ is\ a\ solution\ to\ m^4=20.$  

• true

• false

Lin is saving $300 per year in an account that pays 4.5% interest per year, compounded annually. About how much money will she have 20 years after she started?

• $545.45

• $3,748.78

• $9,411.43

• $1,124,634.54