danny purchased a new camper for $47,000. this particular brand of camper decreases in value by…

danny purchased a new camper for $47,000. this particular brand of camper decreases in value by approximately 11.5% per year. what is the best estimate of the value of danny’s camper after 4 years? $72,643.60 $24,534.29 $28,831.75 $32,578.24 20 pts

danny purchased a new camper for $47,000. this particular brand of camper decreases in value by approximately 11.5% per year. what is the best estimate of the value of danny’s camper after 4 years? $72,643.60 $24,534.29 $28,831.75 $32,578.24 20 pts

Answer

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of decay as a decimal, and $t$ is the number of time - periods. Here, $P=$47000$, $r = 0.115$, and $t = 4$.

Step2: Substitute the values into the formula

$A=47000\times(1 - 0.115)^4$. First, calculate $1-0.115 = 0.885$. Then, $(0.885)^4=0.885\times0.885\times0.885\times0.885\approx0.608176$.

Step3: Calculate the final value

$A = 47000\times0.608176\approx28584.27$. The closest value to this in the options is $$28831.75$.

Answer:

$28831.75$