Question

select the three be represented by an exponential function.
a. snow was of 3.5 inches per hour
b. a music service has a fixed monthly cost and charges $0.20 for each downloaded song.
c. a coin collection appreciates at a rate of 17% per year
d. a car depreciates at a rate of 2.5% per year.
e. money invested in a savings account grows at an annual rate of 3.4%

Explanation:

To determine which situations are represented by exponential functions, we analyze each option:

• Option A: Snow falling at a constant rate of 3.5 inches per hour represents a linear function (constant rate of change), not exponential.
• Option B: A music service with a fixed monthly cost and a per - song charge is a linear function (total cost = fixed cost + (cost per song × number of songs)), not exponential.
• Option C: A coin collection appreciating at a rate of 17% per year. The value of the coin collection each year is a percentage of the previous year's value. If the initial value is \( V_0 \), the value after \( t \) years is \( V(t)=V_0(1 + 0.17)^t \), which is an exponential growth function.
• Option D: A car depreciating at a rate of 2.5% per year. If the initial value of the car is \( V_0 \), the value after \( t \) years is \( V(t)=V_0(1 - 0.025)^t \), which is an exponential decay function.
• Option E: Money invested in a savings account growing at an annual rate of 3.4%. If the initial investment is \( P_0 \), the amount after \( t \) years is \( A(t)=P_0(1 + 0.034)^t \), which is an exponential growth function.

So the three situations represented by exponential functions are C, D, and E.

Answer:

C. A coin collection appreciates at a rate of 17% per year
D. A car depreciates at a rate of 2.5% per year
E. Money invested in a savings account grows at an annual rate of 3.4%