the general equation for depreciation is given by y = a(1 - r)^t, where y = current value, a = original…

the general equation for depreciation is given by y = a(1 - r)^t, where y = current value, a = original cost, r = rate of depreciation, and t = time, in years.\nthe original value of a car is $24,000. it depreciates 15% annually. what is its value in 4 years? $

the general equation for depreciation is given by y = a(1 - r)^t, where y = current value, a = original cost, r = rate of depreciation, and t = time, in years.\nthe original value of a car is $24,000. it depreciates 15% annually. what is its value in 4 years? $

Answer

Explanation:

Step1: Identify the values

$A = 24000$, $r=0.15$, $t = 4$

Step2: Substitute into the formula

$y=A(1 - r)^t=24000\times(1 - 0.15)^4$

Step3: Calculate $(1 - 0.15)$

$1-0.15 = 0.85$

Step4: Calculate $(0.85)^4$

$(0.85)^4=0.85\times0.85\times0.85\times0.85 = 0.52200625$

Step5: Calculate the value of $y$

$y=24000\times0.52200625 = 12528.15$

Answer:

$12528.15$