A new car is purchased for 20700 dollars. The value of the car depreciates at 11 % per year. What will the value of the car be, to the nearest cent, after 11 years.
Answers
Given:
The cost of the new car = $ 20700
The rate of depreciation of the car = 11% per year
To find:
The value of the car, to the nearest cents, after 11 years
Solution:
We know that when there is a decrease in the price of car, machines or certain valuable articles, then to find its value after n years, the following formula can be used:
where
D = value after n years
P = present value
R = rate of decrease
n = no. of years
Now, we will substitute the given values in the formula,
D = 20700
⇒ D = 20700
⇒ D = 20700
⇒ D = 20700 × 0.277517 ...... [0.89¹¹ = 0.277517 calculation done on calculator]
⇒ D = $ 5744.60
Thus, the value of the car after 11 years will be $ 5744.60.
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Answer:
5744.61
Step-by-step explanation:
\text{Exponential Functions:}
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }20700
a=starting value = 20700
r=\text{rate = }11\% = 0.11
r=rate = 11%=0.11
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.11=0.89
b=1−r=1−0.11=0.89
\text{Write Exponential Function:}
Write Exponential Function:
y=20700(0.89)^x
y=20700(0.89)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=20700(0.89)^{11}
y=20700(0.89)
11
y= 5744.6082627
y=5744.6082627
Evaluate
y≈5744.61
y≈5744.61
round