A material has a half-life of 4 hours. A sample of the material is measured to be 225 milligrams at noon.

1. Write an expression to represent the amount of material, in milligrams, 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 material at some time. 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 show 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 \(m^4 = 20\).

Each year, Lin adds \$300 to an account that also pays 4.5% interest, compounded annually. About how much money will she have in the account 20 years after she starts saving?