A new car worth 45K is depreciating in value by 5K per year. How can I write a formula that models the cars' value,y, in dollars, after x years?Then using the formula determine after how many years the cars' value will be 9K.
To write a formula that models the car's value, y, in dollars after x years, we can use the concept of linear depreciation. Since the car's value is decreasing by 5K per year, we know that the value after x years will be 45K minus 5K times x.
So, we can write the formula as:
y = 45K - 5Kx
To determine after how many years the car's value will be 9K, we can substitute the value of y with 9K in the formula and solve for x. Let's do that:
9K = 45K - 5Kx
First, we need to convert the values to the same units. Since 1K is equal to 1000, we can rewrite the equation as:
9000 = 45000 - 5000x
Next, we isolate the variable by moving the constant term to the other side:
5000x = 45000 - 9000
Now, let's simplify the equation:
5000x = 36000
To solve for x, we divide both sides of the equation by 5000:
x = 36000 / 5000
x ≈ 7.2
So, after approximately 7.2 years, the car's value will be 9K.