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Chapter 1: Q28E (page 7)

Sketch a rough graph of the market value of a new car as a function of time for a period of 20 years. Assume the car is well maintained.

Short Answer

Expert verified

Initially, the price of the new vehicle decrease at a faster rate, whereas later, it decreases at a lesser rate.

Step by step solution

01

Find the variation of the amount 

Initially, the price of the new vehicle decrease at a faster rate, whereas later, it decreases at a lesser rate.

02

Sketch the variation of temperature 

The graph below represents the variation in the price of the car with time in years.

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Most popular questions from this chapter

The point \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\) lies on the curve \(y = \frac{{\bf{1}}}{{{\bf{1}} - x}}\).

(a) If Q is the point \(\left( {x,\frac{{\bf{1}}}{{{\bf{1}} - x}}} \right)\), find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

(i) 1.5 (ii) 1.9 (iii) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1(vii) 2.01 (viii) 2.001

(b) Using the results of part (a), guess the value of the slope of tangent line to the curve at \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\).

(c) Using the slope from part (b), find an equation of the tangent line to the curve at \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\).

Sketch the graph of the function

\(f\left( x \right) = \left| {x + {\bf{2}}} \right|\)

A student bought a smartwatch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded t minutes after 3.00 PM on the first day she wore the watch.

t(min)

0

10

20

30

40

Steps

3438

4559

5622

5622

7398

(a) Find the slopes of the secant lines corresponding to given intervals of t. What do these slopes represent?

(i) \(\left( {{\bf{0}},{\bf{40}}} \right)\) (ii) \(\left( {{\bf{10}},{\bf{20}}} \right)\) (iii) \(\left( {{\bf{20}},{\bf{30}}} \right)\)

(b) Estimate the student’s walking pace, in steps per minute, at 3:20 PM by averaging the slopes of two secant lines.

7-14 Determine whether the equation or table defines y as a function of x.

\({x^{\bf{2}}} + {\left( {y - {\bf{3}}} \right)^2} = {\bf{5}}\)

13. Recent studies indicate that the average surface temperature of the Earth has been rising steadily. Some scientists have modeled the temperature by the linear function \(T = 0.02t + 8.50\), where \(T\)is temperature in °C and \(t\)represents years since 1900.

(a) What do the slope and \(T\)-intercept represent?

(b) Use the equation to predict the Earth’s average surface temperature in 2100.
See all solutions

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