Question

homework assignment 6.1 exponential functions
due sunday by 11:59pm points 12 submitting an external tool
homework assignment 6.1 exponential functions
score: 2/12 answered: 2/12
question 3
a vehicle purchased for $27500 depreciates at a constant rate of 6%.
determine the approximate value of the vehicle 10 years after purchase.
round to the nearest whole number.
basic funcs trig
enter a mathematical expression more...

Explanation:

Step1: Identify the formula

The formula for exponential decay is \( A = P(1 - r)^t \), where \( P \) is the initial amount, \( r \) is the rate of decay, and \( t \) is the time.

Step2: Substitute the values

Here, \( P=\$27500 \), \( r = 0.06 \), and \( t = 10 \).
So, \( A=27500\times(1 - 0.06)^{10}=27500\times(0.94)^{10} \).

Step3: Calculate \( (0.94)^{10} \)

Using a calculator, \( (0.94)^{10}\approx0.538615 \).

Step4: Calculate \( A \)

\( A = 27500\times0.538615\approx14812.91 \).

Answer:

\( 14813 \)