Question 14 (3 points)
Han purchased a car for $\$ 35000.00$. The car depreciates by $4 \%$ each year
a) Create an algebraic model to represent this depreciation
b) Use this model to estimate the value of the car after 5 years.

Step 1 ：The depreciation of the car can be modeled using an exponential decay formula. The general formula for exponential decay is: \( P(t) = P_0 * (1 - r)^t \) where: \( P(t) \) is the value of the object at time \( t \), \( P_0 \) is the initial value of the object, \( r \) is the rate of decay, and \( t \) is the time.

Step 2 ：In this case, the initial value of the car (\( P_0 \)) is $35000, the rate of decay (\( r \)) is 4% or 0.04, and we want to find the value of the car after 5 years (\( t = 5 \)).

Step 3 ：Substitute the given values into the formula: \( P(t) = 35000 * (1 - 0.04)^5 \)

Step 4 ：Solving the equation gives the estimated value of the car after 5 years.

Step 5 ：Final Answer: The estimated value of the car after 5 years is approximately $28538.04. Therefore, the final answer is \(\boxed{28538.04}\).