Question

A car is originally worth $43,500. It takes 12 years for this car to totally depreciate a. Write a straight line depreciation equation that models the situation. b.how long will it take for this car to be worth 25% of its value? C.how much will the car be worth in 10 years?

Answer 1

To write the straight line depreciation equation that models the situation, the equation is y = -3625x + 43500. It will take approximately 10.55 years for the car to be worth 25% of its value. In 10 years, the car will be worth $7,250.

Step-by-step explanation:

To write a straight line depreciation equation, we need to determine the equation of a line that represents the decrease in value over time. In this case, the car's value starts at $43,500 and depreciates to $0 over 12 years.

Using the point-slope form of a line, where the initial value is the y-intercept and the decrease in value over time is the slope, the equation is:

y = -3625x + 43500

To find the time it takes for the car to be worth 25% of its value, we can substitute in 0.25 times the original value and solve for x:

0.25(43500) = -3625x + 43500

Simplifying the equation gives us:

-3625x = 43500(0.25) - 43500

Solving for x, the time it takes for the car to be worth 25% of its value, we find:

x = 10.55 years

To find the worth of the car in 10 years, we can substitute 10 for x in the equation and solve for y:

y = -3625(10) + 43500

Simplifying gives us:

y = 43500 - 36250

y = 7250

Answer 2

A: The straight-line depreciation equation is a linear equation of the form:

Value = initial value - (rate of depreciation) x (age)

Where the "rate of depreciation" is the amount by which the value decreases each year. In this case, the initial value is $43,500, and the car depreciates over a period of 12 years. So, you can calculate the rate of depreciation as:

Rate of depreciation = (initial value - final value) / (age)

Where the final value is zero (since the car is totally depreciated after 12 years). Therefore, you have:

Rate of depreciation = ($43,500 - $0) / 12 years = $3,625 per year

Substituting this into the formula, you get:

Value = $43,500 - $3,625 x (age)

Where "value" is the current value of the car after "age" years.

B: You want to find how long it will take for the car to be worth 25% of its value. Let's call this time "t". Then you have:

0.25($43,500) = $10,875 = $43,500 - $3,625t

Solving for "t", you get:

$3,625t = $43,500 - $10,875 = $32,625

t = $32,625 / $3,625 = 9 years

Therefore, it will take 9 years for the car to be worth 25% of its value.

C: You want to find how much the car will be worth in 10 years. Substituting "age = 10" into the equation derived in part A, you get:

Value = $43,500 - $3,625 x 10 = $7,750

Therefore, the car will be worth $7,750 in 10 years.