Solve the following problem:
Kate bought a car for $20,000. A study shows that a car will depreciate (go DOWN in value) by 15% each year. How much is Kate's car worth after 5 years?
a) Formula used: ___________________________________
b) Substitute values: _________________________________
c) Final answer: _____________________________________
d) Does this final answer make sense compared to the original cost of the car? Why?
e) DESCRIBE (using a complete sentence or two) how you can solve this problem graphically.
please help asap!!!!
Since you are taking off 15% each year, at the end of each your you will have 85% or .85 of the previous years amount.
so after 5 years:
20000(.85)^5
= ...
plug in your answers where needed.
right so whats the formula?
a) Formula used: To calculate the depreciation of the car after a certain number of years, we can use the formula: Value after depreciation = Initial value × (1 - Depreciation rate)^Number of years
b) Substitute values: In this case, the initial value of the car is $20,000 and the depreciation rate is 15%. The number of years is 5. Now we can substitute these values into the formula.
c) Final answer: Plugging the values into the formula, we get: Value after depreciation = $20,000 × (1 - 0.15)^5. Evaluating this expression gives us the final answer.
d) Does this final answer make sense compared to the original cost of the car? Why? Yes, the final answer makes sense since the car will depreciate over time. The value after 5 years will be less than the original cost of $20,000.
e) DESCRIBE (using a complete sentence or two) how you can solve this problem graphically: To solve this problem graphically, you can plot a graph with the number of years on the x-axis and the value of the car on the y-axis. Choose specific values for the years (e.g., 1, 2, 3, etc.) and calculate the corresponding values of the car using the given depreciation rate. Plot these points on the graph and draw a line connecting them. The y-coordinate of the point representing 5 years will give you the value of the car after 5 years.