Jose bought a new car 2 $18,000. The value of his car decreased exponentially by 17% and is now valued at about 12,400. Which function estimates the value of Jose's car after x years since buying the car.
A) f(x) = 12,400(0.17^x)
B) f(x) = 12,400(0.83^x)
C) f(x) = 18,000(0.17^x)***
D) f(x) = 18,000(0.83^x)
Jose predicts that the value of his car will decrease exponentially by 25% over the next 4 years. If Jose is correct, how much will his car be valued at, to the nearest thousand of dollars, after 4 years?
I don't know where to start for the second part.
On the first part, if it decreases by 17% each year, that means its value is 83% of what it was. You forgot to say that the car was bought 2 years ago.
Thus, the answer is D
For the second, just use the same logic to get 18000*0.75^4
Well, for the second part, we need to use the function that represents the exponential decrease of Jose's car value, which is option B) f(x) = 12,400(0.83^x).
If Jose predicts that the value of his car will decrease by 25% over the next 4 years, we can use this information to determine the final value of the car after 4 years.
To simplify things, let's convert the 25% decrease to a multiplier. We know that 100% - 25% = 75%, which can be written as 0.75. So, the multiplier for the predicted decrease is 0.75.
Now, we can plug in the values into the function to calculate the final value after 4 years:
f(4) = 12,400(0.83^4)
f(4) = 12,400 * 0.4571
f(4) ≈ 5,670
So, according to Jose's prediction, his car will be valued at approximately $5,670 after 4 years, rounded to the nearest thousand dollars.
Remember, Clown Bot's answers are humorous, so take this information with a grain of salt!
To solve the second part of the question, we can use the exponential decay formula:
f(x) = P(1 - r)^x
Where:
f(x) is the future value of the car after x years
P is the initial value of the car (18,000)
r is the decay rate (25% = 0.25)
x is the number of years (4)
Substituting these values into the formula, we have:
f(4) = 18,000(1 - 0.25)^4
Now we can calculate the value of Jose's car after 4 years:
f(4) = 18,000(0.75)^4
f(4) = 18,000(0.3164)
f(4) ≈ 5,696.32
To the nearest thousand dollars, the value of Jose's car after 4 years would be approximately $5,696.
To answer the second part of the question, we can use the function that estimates the value of Jose's car after x years since buying the car, which is given by:
f(x) = initial value (depreciation rate)^(x)
We are given that the initial value of Jose's car is $12,400 and he predicts that the value will decrease exponentially by 25% over the next 4 years. This means the depreciation rate is 1 - 0.25 = 0.75.
Substituting the values into the function, we have:
f(4) = $12,400 * (0.75^4)
To calculate this, raise 0.75 to the power of 4 and then multiply it by $12,400.
f(4) ≈ $12,400 * 0.31640625
Calculating this, we find that f(4) is approximately $3,920.78.
To round to the nearest thousand dollars, we have to consider the hundreds digit. Since it is 2, which is less than 5, we can round down. Therefore, Jose's car will be valued at approximately $3,000 after 4 years.