Alex collects coins that appreciate (increase in) value. At the store he has found three coins that he likes and can afford. Help Alex decide which coin to buy by selecting two coins and comparing their values over time. Coin A Coin B

Finding Equations for the Values

2. What are the current values and appreciation rates of the two coins you selected? (2 points: 1 point for each of 2 coins)

Coin- Current Value- Annual Appreciation Rate-

Coin- Current Value- Annual Appreciation Rate-

3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use the formula:

V(t) = P(1 + r)t, where V(t) is the value of the coin in t years, P is the initial investment, and r is the growth rate.

For each of the coins you selected, identify P and r, then set up an equation to find the value of the coin at any t. (2 points: 1 point for each coin)

Coin P r Function

V(t) =

V(t) =

Interpreting Exponential Expressions

4. In the coin value formula, V(t) = P(1 + r)t, which part(s) form the base of the exponential function? Which part(s) form the constant, or initial value? Which part(s) form the exponent? (4 points: 1 point for each answer below)

Base:

Constant, or initial value:

Exponent:

In this function, if the value of r were to increase, would the value represented by P also increase or stay the same? Why? Explain your answer using terms such as "rate of growth" and "initial value" in the context of the coin problem.

5. Find the value of the coins after 10, 20, 30, and 60 years. Use the function you identified in question 3 to calculate the value. (8 points: 1 point for each time interval)

Coin A Coin B

Initial Value

10 years

20 years

30 years

60 years

Determining the More Valuable Coin

6. Which coin is more valuable after 10 years? 20 years? 30 years? 60 years? Which coin would you purchase if you intended to keep it longer than 60 years, and why? (Hint: Look at r.)

(4 points: 0.5 point each for identifying the more valuable coin; 2 points for the last question)