Question

A new car is purchased for $30,000 and overtime it’s value depreciates by 1/2 every six years. how long to the nearest 10th of the year would it take for the value of the car to be $3500

Answer 1

To find out how long it would take for the value of the car to reach $3500, we can set up an equation and solve for x. The equation is $3500 = $30000 * (1/2)^x. Using logarithmic properties, we can find that x is approximately (log($3500) - log($30000)) / log(1/2).

Step-by-step explanation:

To find out how long it would take for the value of the car to reach $3500, we can set up an equation. Let x represent the number of six-year periods. The value of the car after x six-year periods can be represented by the equation:

V = $30000 * (1/2)^x

We want to find the value of x when V = $3500. Plugging in the values, the equation becomes:

$3500 = $30000 * (1/2)^x

To solve for x, we can take the logarithm of both sides:

log($3500) = log($30000 * (1/2)^x)

Using logarithmic properties, we can simplify this to:

log($3500) = log($30000) + x * log(1/2)

Next, we can isolate x by subtracting log($30000) from both sides:

x * log(1/2) = log($3500) - log($30000)

Finally, we can solve for x by dividing both sides by log(1/2):

x = (log($3500) - log($30000)) / log(1/2)

We can use a calculator to find the approximate value of x.