Lesson 4

A bacteria population is tripling every hour. By what factor does the population change in \(\frac12\) hour? Select all that apply.

\(\sqrt3\)

\(\frac32\)

\(\sqrt[3]{2}\)

\(3^\frac12\)

\(3^2\)

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.

1. Write an expression to represent the amount of medication, in milligrams, in the patient’s body at:
   1. 1 p.m. on the same day
   2. 7 p.m. on the same day
2. The expression \(225 \boldcdot \left(\frac12\right)^{\frac52}\) represents the amount of medicine in the body some time after it is administered. What is that time?

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

1. Each month?
2. Every 3 months?
3. Every 20 months?

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. Write an expression to represent the car’s value 4 years after purchase.
3. By what factor is the value of the car changing each year? Show your reasoning.

The value of a stock increases by 8% each year. 

1. Explain why the stock value does not increase by 80% each decade.
2. Does the value increase by more or less than 80% each decade?

Decide if each statement is true or false.

1. \(50^\frac12 = 25\)
2. \(\sqrt{30}\) is a solution to \(y^2 = 30\).
3. \(243^{\frac13}\) is equivalent to \(\sqrt[3]{243}\).
4. \(\sqrt{20}\) is a solution to \(m^4 = 20\).

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