The formula for the value of a car, C, after t years of depreciation of its initial value v at a rate of r is C=v(1−r)t.
A: How can you rewrite the formula to correctly isolate v?
B: What was the initial value of the car (to the nearest dollar) if it depreciated 10% each year for 10 consecutive years and has a current value of $8,019.60? Select one answer for question A, and one answer for question B. Below are your answers
B: $2,796
A: (1−r)t=v
B: $27,963
B: $23,000
A: C+(1−r)t=v
B: $80,199
B: $8,020
B: $8,019
B: $80,193
A: c(1−r)t=v
A: −(1−r)t=v
So I tried to do this 2 times but I got 2 complete different answers. I don't know what step I'm doing wrong.
The First time I got
A: (1−r)t=v
B: $8,019
Second time I got
c(1−r)t=v
B:$2,796
I tried different formulas because I did not know the format I need to use, Can someone please help me?
You forgot the exponent
C=v (1−r)^t
where v is initial value and C is value after t years
so
v = C / (1-r)^t = C (1-r)^-t
v = 8019.60 / (0.90)^10
= 8019.60 / 0.34868
= 22,999.88 or about 23 thousand
Oh no, wow thank you so much Mr. Damon! I failed the test haha but this will definitely help in the future to make sure to watch my steps!
To correctly isolate v in the formula C = v(1−r)^t, you need to divide both sides of the equation by (1−r)^t. Let's go through the steps:
Step 1: Start with the formula C = v(1−r)^t.
Step 2: Divide both sides of the equation by (1−r)^t. This will give you C / (1−r)^t = v.
So the correct answer for question A is: (1−r)^t = v.
Now let's move on to question B.
Given that the current value of the car is $8,019.60 and it has depreciated 10% each year for 10 consecutive years, we can substitute the values into the formula to find the initial value, v.
Step 1: Write the formula as C = v(1−r)^t.
Step 2: Substitute the given values: C = $8,019.60, r = 10% = 0.10, t = 10.
The formula becomes $8,019.60 = v(1−0.10)^10.
Step 3: Simplify the formula: $8,019.60 = v(0.90)^10.
Step 4: Calculate (0.90)^10 ≈ 0.3487.
Substituting this value back into the equation, we have $8,019.60 = v * 0.3487.
Step 5: Divide both sides of the equation by 0.3487 to solve for v: v ≈ $8,019.60 / 0.3487.
Using a calculator, we find that v ≈ $22,989.10.
So the correct answer for question B is: $22,989 (to the nearest dollar).
It seems like you made a mistake in your calculations, resulting in different answers. Make sure to double-check your calculations and follow each step correctly to get the accurate answer.