Several years ago, ADTF Distributors purchased a brand new cargo plane to increase their coast to coast shipping capabilities. When the plane was new, it was valued at 135 millon dollars. However, it has depreciated in value over time. After owning and using the plane for 6 years, ADTF had It inspected and found that it was now valued at 118 million dollars. Let V(t) give the value of the cargo plane in milions of dollars, where t is the number of years since the plane was purchased. Assurne V(t) follows an exponential model of the form v(e) - (b)". (a) Translate the information given in the first paragraph above into two data points for the function V(t). List the point that corresponds to the original purchase first. V( V( (b) Next, we will find the two missing parameters for V(0). First, Then, using the second point from part (a), solve for b. Round to 4 decimal places. Note make sure you have b accurate to 4 decimal places before proceeding Use this rounded value for b for all the remaining atepa. (G) Wite the function V(). V(1) = (d) Estimate the value of the plane 19 years after the purchase (round to 2 decimal places). According to our model, 19 years after ADTF purchased the plane, It has a value of milion dollars. (e) How many years until the value of the plane is down to 70 million dollars? Solve for t rounded to 2 decimal places.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Transcribed Image Text:Several years ago, ADTF Distributors purchased a brand new cargo plane to increase their coast to coast shipping capabilities. When the plane was new, it was valued at 135 millon dollars. However, it has depreciated in value over time. After owning and using the plane for 6 years, ADTF had It inspected and found that it was now valued at 118 million dollars. Let V(t) give the value of the cargo plane in milions of dollars, where t is the number of years since the plane was purchased. Assurne V(t) follows an exponential model of the form v(e) - (b)". (a) Translate the information given in the first paragraph above into two data points for the function V(t). List the point that corresponds to the original purchase first. V( V( (b) Next, we will find the two missing parameters for V(0). First, Then, using the second point from part (a), solve for b. Round to 4 decimal places. Note make sure you have b accurate to 4 decimal places before proceeding Use this rounded value for b for all the remaining atepa. (G) Wite the function V(). V(1) = (d) Estimate the value of the plane 19 years after the purchase (round to 2 decimal places). According to our model, 19 years after ADTF purchased the plane, It has a value of milion dollars. (e) How many years until the value of the plane is down to 70 million dollars? Solve for t rounded to 2 decimal places.

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