Studdy AI Logo
Math

QuestionA company buys a robot for \$87,000. Analyze its 8-year depreciation data and answer the following:
a. Identify the function type and write a linear function for value VV over time tt. b. Graph the function and explain straight line depreciation. c. Interpret the slope and intercepts. d. Find a real-life example of straight line depreciation, model it, and graph it.

Studdy Solution

STEP 1

Assumptions1. The initial value of the robot is $87,000. The value of the robot depreciates linearly over an8-year period3. The value of the robot at the end of each year is given in the table

STEP 2

First, we need to determine the type of function that represents the data. By observing the table, we can see that the value of the robot decreases by a constant amount each year. This suggests that the function is a linear function.

STEP 3

To write a linear function, we need to find the slope and the y-intercept. The slope is the rate of change, which is the change in the value of the robot divided by the change in time.
lope=Change in valueChange in timelope = \frac{Change\, in\, value}{Change\, in\, time}

STEP 4

We can calculate the slope using the values from the first two years.
lope=$79,750−$87,0001−0lope = \frac{\$79,750 - \$87,000}{1 -0}

STEP 5

Calculate the slope.
lope=−$7,2501=−$7,250lope = \frac{-\$7,250}{1} = -\$7,250

STEP 6

The y-intercept is the value of the robot at time0, which is $87,000.

STEP 7

Now we can write the linear function. The general form of a linear function is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
V(t)=−$7,250t+$87,000V(t) = -\$7,250t + \$87,000

STEP 8

To sketch a graph of the function, plot the initial value at time0 and use the slope to determine the value at each subsequent year. The graph will be a straight line that decreases from left to right, which is why this type of depreciation is called straight line depreciation.

STEP 9

The slope of the graph, -\$7,250, represents the amount the value of the robot decreases each year. The y-intercept, \$87,000, represents the initial value of the robot.

STEP 10

For part d, an example of straight line depreciation could be a car that was purchased for \20,000anddepreciatesby$2,000eachyear.Thefunctionthatmodelsthisexamplewouldbe20,000 and depreciates by \$2,000 each year. The function that models this example would beV(t)=−$2,000t+$20,000V(t) = -\$2,000t + \$20,000$The graph of this function would be a straight line that starts at \$20,000 and decreases by \$2,000 each year.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord