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.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.