A charity organization plans a fall fund-raiser for heart research. It knows that the profit will vary according to the price of the tickets. The graph below shows the profit, in thousand dollars, from the sale of tickets to the fund-raiser at various ticket prices, in dollars. TP() thousand dollars 15 10 x dollars 10 20 30 40 50 60 70 80 90 100110120130 140150160170 Use a ruler to draw an accurate tangent line to the graph at a ticket price of $70. a. b. Calculate the instantaneous rate of change at point P(x) when x 70, by choosing two points on the tangent line and then calculating the slope of the tangent line. Include units with the (80, ) answer (70,(4) P'(70)= C. Find P'(70) and include units with the answer. Rewrite the answer to part c) using differential notation. d. e. Write a sentence of interpretation for the derivative of P(x) when x = 70 . 5 f. Find the percentage rate of change of P(x) when x = 70 and write a sentence of interpretation. Is the profit changing more quickly when the charity sets the ticket price at $50 or at $70? Explain by using tangent slopes. g.
A charity organization plans a fall fund-raiser for heart research. It knows that the profit will vary according to the price of the tickets. The graph below shows the profit, in thousand dollars, from the sale of tickets to the fund-raiser at various ticket prices, in dollars. TP() thousand dollars 15 10 x dollars 10 20 30 40 50 60 70 80 90 100110120130 140150160170 Use a ruler to draw an accurate tangent line to the graph at a ticket price of $70. a. b. Calculate the instantaneous rate of change at point P(x) when x 70, by choosing two points on the tangent line and then calculating the slope of the tangent line. Include units with the (80, ) answer (70,(4) P'(70)= C. Find P'(70) and include units with the answer. Rewrite the answer to part c) using differential notation. d. e. Write a sentence of interpretation for the derivative of P(x) when x = 70 . 5 f. Find the percentage rate of change of P(x) when x = 70 and write a sentence of interpretation. Is the profit changing more quickly when the charity sets the ticket price at $50 or at $70? Explain by using tangent slopes. g.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 81E
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I need help with my paper homework im confused and dont know what im doing.
Transcribed Image Text:A charity organization plans a fall fund-raiser for heart research. It knows that the profit will
vary according to the price of the tickets. The graph below shows the profit, in thousand
dollars, from the sale of tickets to the fund-raiser at various ticket prices, in dollars.
TP() thousand dollars
15
10
x dollars
10 20 30 40 50 60 70 80 90 100110120130 140150160170
Use a ruler to draw an accurate tangent line to the graph at a ticket price of $70.
a.
b. Calculate the instantaneous rate of change at point P(x) when x 70, by choosing two points
on the tangent line and then calculating the slope of the tangent line. Include units with the
(80, )
answer
(70,(4)
P'(70)=
C. Find P'(70) and include units with the answer.
Rewrite the answer to part c) using differential notation.
d.
e. Write a sentence of interpretation for the derivative of P(x) when x = 70 .
5
Transcribed Image Text:f. Find the percentage rate of change of P(x) when x = 70 and write a sentence of
interpretation.
Is the profit changing more quickly when the charity sets the ticket price at $50 or at $70?
Explain by using tangent slopes.
g.
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